appendix second pass future value concepts...
TRANSCRIPT
Second Pass
Future Value of a Single Amount In situations involving the future value of a single amount, you are asked to calculate
how much money you will have in the future as a result of investing a certain amount
at the present time. If you were to receive a gift of $10,000, for instance, you might
decide to put it in a savings account and use the money as a down payment on a house
when you graduate. The future value computation will tell you how much money
would be available when you graduate.
To solve a future value problem, you need to know three items:
1. The amount to be invested .
2. The interest rate ( i ) that the amount will earn.
3. The number of periods ( n ) in which the amount will earn interest .
Since the future value concept is based on compound interest, the amount of interest
for each period is calculated by multiplying the interest rate by the principal plus any
interest not paid out in prior periods. Graphically, the calculation of the future value
of $1 for three periods and an interest rate of 4 percent may be represented as follows:
Presenttime$1
Futurevalue$1.125
Interest accumulatesover time
1 2 3
Assume that on January 1, 2014, you deposit $1,000 in a savings account at
4 percent annual interest, compounded annually. At the end of three years, the $1,000
will have increased to $1,124.90 as follows:
Year
Amount at
Start of Year 1
Interest
During the Year 5
Amount at
End of Year
2014 $1,000.0 1 $1,000.0 3 4% 5 $40 5 $1,040.0
2015 1,040.0 1 1,040.0 3 4% 5 $41.6 5 1,081.6
2016 1,081.6 1 1,081.6 3 4% 5 $43.3 5 1,124.9
We can avoid the detailed arithmetic by referring to Table 10E.1 , Future Value of
$1. For i 5 4% and n 5 3, we find the value 1.1249. We then compute the balance at
the end of year 3 as follows:
$1,000 3 1.1249 5 $1,124.90
From Table 10E.1,
Interest rate 5 4%
n 5 3
Note that the increase of $124.9 is due to the time value of money. It is inter-
est revenue to the owner of the savings account and interest expense to the savings
institution.
A P P E N D I X
10E Future Value Concepts
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Second Pass
10E-2 APPENDIX 10E Future Value Concepts
FUTURE VALUE OF AN ANNUITY If you are saving money for some purpose, such as a new car or a trip to Europe, you
might decide to deposit a fixed amount of money in a savings account each month.
The future value of an annuity computation will tell you how much money will be in
your savings account at some point in the future.
The future value of an annuity includes compound interest on each payment from
the date of payment to the end of the term of the annuity. Each new payment accumu-
lates less interest than prior payments only because the number of periods remaining
to accumulate interest decreases. The future value of an annuity of $1 for three periods
at 4 percent may be represented graphically as follows:
Future valueof an annuity
$3.12
1 2 3$1 $1 $1
=
Assume that you deposit $1,000 cash in a savings account each year for three years
at 4 percent interest per year (i.e., a total principal of $3,000). You make the first
$1,000 deposit on December 31, 2014, the second deposit on December 31, 2015,
and the third and last one on December 31, 2016. The first deposit earns compound
interest for two years (for a total principal and interest of $1,081.6), the second deposit
earns interest for one year (for a total principal and interest of $1,040), and the third
deposit earns no interest because it was made on the day that the balance is computed.
Thus, the total amount in the savings account at the end of three years is $3,121.6
($1,081.6 1 $1,040 1 $1,000).
To derive the future value of this annuity, we could compute the interest on each
deposit. However, we can refer to Table 10E.2 , Future Value of an Annuity of $1 for
i 5 4% and n 5 3 to find the value 3.1216. The future value of your three deposits of
$1,000 each can be computed as follows:
$1,000 3 3.1216 5 $3,121.60
From Table 10E.2,
Interest rate 5 4%
n 5 3
THE POWER OF COMPOUNDING Compound interest is a remarkably powerful economic force. The ability to earn
interest on interest is the key to building economic wealth. If you start your career
on your 22nd birthday and save $1,000 per year for 10 years at an interest rate of
5 percent compounded annually until you retire at the end of your 65th year of
age, you will accumulate a total of $69,390. The money saved is $10,000 and the rest
is interest that accumulated over the 44-year period from the time you started saving
until the time you retired. If the money saved earns 6 percent instead of 5 percent
throughout the 44-year period, then the total amount increases to $101,309 on your
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Second Pass
10E-3APPENDIX 10E Future Value Concepts
66th birthday, a hefty birthday present! However, if you continue to save $1,000 per year
for 44 years and earn 5 percent interest per year, then your retirement fortune jumps to
$158,700; $44,000 is money saved and the rest is compound interest. The power of com-
pounding in this specific case is illustrated in the graph below. The lesson associated with
compound interest is clear: even though it’s hard to do, you should start saving money now.
20,000
01 4 7 10 13 16 19 22 25 28 31 34 4037 43
40,000
60,000
80,000
100,000
120,000
140,000
160,000
180,000
Year
Dol
lar
Am
ount
Effect of Compound Interest
Money SavedFuture Value of Investment
EXERCISES
Computing Four Kinds of Present and Future Value On January 1, 2014, Wesley Company completed the following transactions (assume an annual
compound interest rate of 6 percent):
a. Deposited $12,000 in Fund A.
b. Established Fund B by agreeing to make six annual deposits of $2,000 each. Deposits are made
each December 31.
c. Established Fund C by depositing a single amount that will increase to $40,000 by the end of
year 7.
d. Decided to deposit a single sum in Fund D that will provide 10 equal annual year-end payments
of $15,000 to a retired employee (payments starting December 31, 2014).
Required (show computations and round to the nearest dollar): 1. What will be the balance of Fund A at the end of year 9?
2. What will be the balance of Fund B at the end of year 6?
3. What single amount must be deposited in Fund C on January 1, 2014?
4. What single sum must be deposited in Fund D on January 1, 2014?
Computing Growth in a Savings Account: A Single Amount On January 1, 2014, you deposited $6,000 in a savings account. The account will earn an annual
compound interest rate of 4 percent, which will be added to the fund balance at the end of each year.
Required (round to the nearest dollar): 1. What will be the balance in the savings account at the end of 10 years?
2. What is the interest for the 10 years?
3. How much interest revenue did the fund earn in 2014? 2015?
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Second Pass
10E-4 APPENDIX 10E Future Value Concepts
Recording Growth in a Savings Account with Equal Periodic Payments You plan to deposit $2,000 in a savings account on each December 31. The account will earn an
annual interest rate of 9 percent, which will be added to the fund balance at year-end. The first
deposit will be made on December 31, 2014 (end of period).
Required (show computations and round to the nearest dollar): 1. Prepare the required journal entry on December 31, 2014, assuming you keep books to account
for your personal finances.
2. What will be the balance in the savings account at the end of the 10th year (i.e., after 10
deposits)?
3. What is the interest earned on the 10 deposits?
4. How much interest revenue did the fund earn in 2015? 2016?
5. Prepare all required journal entries at the end of 2015 and 2016.
Computing Growth for a Savings Fund with Periodic Deposits On January 1, 2014, you decided to plan for a trip around the world upon graduation four years
from now. Your grandmother wants to deposit sufficient funds for this trip in a savings account for
you. You estimate that the trip would cost $15,000. To be generous, your grandmother decided to
deposit $3,500 in the fund at the end of each of the next four years, starting on December 31, 2014.
The savings account will earn interest at an annual rate of 6 percent, which will be added to the
savings account at each year-end.
Required (show computations and round to the nearest dollar): 1. How much money will you have for the trip at the end of year 4 (i.e., after four deposits)?
2. What is the interest for the four years?
3. How much interest revenue did the fund earn in 2014, 2015, 2016, and 2017?
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E10E–4
PROBLEMS
Computing Present and Future Values On January 1, 2014, Perrakis Company completed the following transactions and events (use an 8
percent annual interest rate for all transactions and assume annual compounding unless otherwise
stated):
a. Deposited $60,000 in a debt retirement fund. Interest will be computed at six-month intervals and
added to the fund at those times (i.e., semi-annual compounding). ( Hint: Think carefully about n
and i. )
b. Established a plant-addition fund of $400,000 to be available at December 31, 2015. A single
sum that will grow to $400,000 will be deposited on January 1, 2014.
c. Established a pension retirement fund of $1,000,000 to be available by December 31, 2016, by
making six equal annual deposits at year-end, starting on December 31, 2014.
d. Purchased an $180,000 machine on January 1, 2014, and paid cash, $80,000. A four-year note
payable is signed for the balance. The note will be paid in four equal year-end amounts starting
on December 31, 2014.
Required (show computations and round to the nearest dollar): 1. In transaction ( a ), what will be the balance in the fund at the end of year 4? What is the total
amount of interest revenue that will be earned during the first four years?
2. In transaction ( b ), what amount must the company deposit on January 1, 2014? What is the total
amount of interest revenue that will be earned by the end of year 5?
3. In transaction ( c ), what is the required amount of each of the six equal annual deposits? What is
the total amount of interest revenue that will be earned over the six years?
4. In transaction ( d ), what is the amount of each of the equal annual payments that will be paid on
the note? What is the total amount of interest expense that will be incurred during the four years?
Prepare journal entries to record the purchase of the machine and the payments on December 31,
2014 and 2015.
P10E–1
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Second Pass
10E-5APPENDIX 10E Future Value Concepts
Computing Present and Future Values On January 1, 2014, Nader Company completed the following transactions (use an annual interest
rate of 6 percent for all transactions):
a. Deposited $300,000 in a debt retirement fund. Interest will be computed at six-month intervals
and added to the fund at those times (i.e., semi-annual compounding). ( Hint: Think carefully
about n and i. )
b. Established a plant-addition fund of $800,000 to be available at the end of year 10. A single sum
that will grow to $800,000 will be deposited on January 1, 2014.
c. Established a pension retirement fund of $600,000 to be available by the end of year 10 by
making 10 equal annual deposits at year-end, starting on December 31, 2014.
d. Purchased a $750,000 machine on January 1, 2014, and paid cash, $350,000. A four-year note
payable is signed for the balance. The note will be paid in four equal year-end amounts, starting
on December 31, 2014.
Required (show computations and round to the nearest dollar): 1. In transaction ( a ), what will be the balance in the fund at the end of year 5? What is the total
amount of interest revenue that will be earned during the first five years?
2. In transaction ( b ), what amount must the company deposit on January 1, 2014? What is the total
amount of interest revenue that will be earned by the end of year 10?
3. In transaction ( c ), what is the required amount of each of the 10 equal annual deposits? What is
the total amount of interest revenue that will be earned over the 10 years?
4. In transaction ( d ), what is the amount of each of the equal annual payments that will be paid on
the note? What is the total amount of interest expense that will be incurred during the four years?
Prepare journal entries to record the purchase of the machine and the payments on December 31,
2014 and 2015.
Computing Amounts for a Fund with Journal Entries On January 1, 2014, Jalopy Company decided to accumulate a fund to build an addition to its plant.
The company will deposit $230,000 in the fund at each year-end, starting on December 31, 2014.
The fund will earn 9 percent interest, which will be added to the fund balance at each year-end. The
fiscal year ends on December 31.
Required: 1. What will be the balance in the fund immediately after the December 31, 2016, deposit?
2. Complete the following fund accumulation schedule:
P10E–2
P10E–3
Date
Cash
Payment
Interest
Revenue
Increase
in Fund
Fund
Balance
31/12/2014
31/12/2015
31/12/2016
Total
3. Prepare adjusting journal entries on December 31 of each of the three years.
4. The plant addition was completed on January 1, 2017, for a total cost of $749,000. Prepare the
journal entry, assuming that this amount is paid in full to the contractor.
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Second Pass
10E-6 APPENDIX 10E Future Value Concepts
Periods 1.5% 1.75% 2% 2.25% 2.5% 2.75% 3% 3.25% 3.5%
1 1.0150 1.0175 1.0200 1.0225 1.0250 1.0275 1.0300 1.0325 1.0350
2 1.0302 1.0353 1.0404 1.0455 1.0506 1.0558 1.0609 1.0661 1.0712
3 1.0457 1.0534 1.0612 1.0690 1.0769 1.0848 1.0927 1.1007 1.1087
4 1.0614 1.0719 1.0824 1.0931 1.1038 1.1146 1.1255 1.1365 1.1475
5 1.0773 1.0906 1.1041 1.1177 1.1314 1.1453 1.1593 1.1734 1.1877
6 1.0934 1.1097 1.1262 1.1428 1.1597 1.1768 1.1941 1.2115 1.2293
7 1.1098 1.1291 1.1487 1.1685 1.1887 1.2091 1.2299 1.2509 1.2723
8 1.1265 1.1489 1.1717 1.1948 1.2184 1.2424 1.2668 1.2916 1.3168
9 1.1434 1.1690 1.1951 1.2217 1.2489 1.2765 1.3048 1.3336 1.3629
10 1.1605 1.1894 1.2190 1.2492 1.2801 1.3117 1.3439 1.3769 1.4106
11 1.1779 1.2103 1.2434 1.2773 1.3121 1.3477 1.3842 1.4216 1.4600
12 1.1956 1.2314 1.2682 1.3060 1.3449 1.3848 1.4258 1.4678 1.5111
13 1.2136 1.2530 1.2936 1.3354 1.3785 1.4229 1.4685 1.5156 1.5640
14 1.2318 1.2749 1.3195 1.3655 1.4130 1.4620 1.5126 1.5648 1.6187
15 1.2502 1.2972 1.3459 1.3962 1.4483 1.5022 1.5580 1.6157 1.6753
16 1.2690 1.3199 1.3728 1.4276 1.4845 1.5435 1.6047 1.6682 1.7340
17 1.2880 1.3430 1.4002 1.4597 1.5216 1.5860 1.6528 1.7224 1.7947
18 1.3073 1.3665 1.4282 1.4926 1.5597 1.6296 1.7024 1.7784 1.8575
19 1.3270 1.3904 1.4568 1.5262 1.5987 1.6744 1.7535 1.8362 1.9225
20 1.3469 1.4148 1.4859 1.5605 1.6386 1.7204 1.8061 1.8958 1.9898
Periods 3.75% 4% 4.5% 5% 6% 7% 8% 9% 10%
1 1.0375 1.0400 1.0450 1.0500 1.0600 1.0700 1.0800 1.0900 1.1000
2 1.0764 1.0816 1.0920 1.1025 1.1236 1.1449 1.1664 1.1881 1.2100
3 1.1168 1.1249 1.1412 1.1576 1.1910 1.2250 1.2597 1.2950 1.3310
4 1.1587 1.1699 1.1925 1.2155 1.2625 1.3108 1.3605 1.4116 1.4641
5 1.2021 1.2167 1.2462 1.2763 1.3382 1.4026 1.4693 1.5386 1.6105
6 1.2472 1.2653 1.3023 1.3401 1.4185 1.5007 1.5869 1.6771 1.7716
7 1.2939 1.3159 1.3609 1.4071 1.5036 1.6058 1.7138 1.8280 1.9487
8 1.3425 1.3686 1.4221 1.4775 1.5938 1.7182 1.8509 1.9926 2.1436
9 1.3928 1.4233 1.4861 1.5513 1.6895 1.8385 1.9990 2.1719 2.3579
10 1.4450 1.4802 1.5530 1.6289 1.7908 1.9672 2.1589 2.3674 2.5937
11 1.4992 1.5395 1.6229 1.7103 1.8983 2.1049 2.3316 2.5804 2.8531
12 1.5555 1.6010 1.6959 1.7959 2.0122 2.2522 2.5182 2.8127 3.1384
13 1.6138 1.6651 1.7722 1.8856 2.1329 2.4098 2.7196 3.0658 3.4523
14 1.6743 1.7317 1.8519 1.9799 2.2609 2.5785 2.9372 3.3417 3.7975
15 1.7371 1.8009 1.9353 2.0789 2.3966 2.7590 3.1722 3.6425 4.1772
16 1.8022 1.8730 2.0224 2.1829 2.5404 2.9522 3.4259 3.9703 4.5950
17 1.8698 1.9479 2.1134 2.2920 2.6928 3.1588 3.7000 4.3276 5.0545
18 1.9399 2.0258 2.2085 2.4066 2.8543 3.3799 3.9960 4.7171 5.5599
19 2.0127 2.1068 2.3079 2.5270 3.0256 3.6165 4.3157 5.1417 6.1159
20 2.0882 2.1911 2.4117 2.6533 3.2071 3.8697 4.6610 5.6044 6.7275
Table 10E.1Future Value of $1, f 5 (1 1 i)n
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Second Pass
10E-7APPENDIX 10E Future Value Concepts
Table 10E.2Future Value of Annuity of $1
(ordinary), F 5 [(1 1 i)n 2 1]/i
Periods* 1.5% 1.75% 2% 2.25% 2.5% 2.75% 3% 3.25% 3.5%
1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
2 2.0175 2.0150 2.0200 2.0225 2.0250 2.0275 2.0300 2.0325 2.0350
3 3.0528 3.0452 3.0604 3.0680 3.0756 3.0833 3.0909 3.0986 3.1062
4 4.1062 4.0909 4.1216 4.1370 4.1525 4.1680 4.1836 4.1993 4.2149
5 5.1781 5.1523 5.2040 5.2301 5.2563 5.2827 5.3091 5.3357 5.3625
6 6.2687 6.2296 6.3081 6.3478 6.3877 6.4279 6.4684 6.5091 6.5502
7 7.3784 7.3230 7.4343 7.4906 7.5474 7.6047 7.6625 7.7207 7.7794
8 8.5075 8.4328 8.5830 8.6592 8.7361 8.8138 8.8923 8.9716 9.0517
9 9.6564 9.5593 9.7546 9.8540 9.9545 10.0562 10.1591 10.2632 10.3685
10 10.8254 10.7027 10.9497 11.0757 11.2034 11.3328 11.4639 11.5967 11.7314
11 12.0148 11.8633 12.1687 12.3249 12.4835 12.6444 12.8078 12.9736 13.1420
12 13.2251 13.0412 13.4121 13.6022 13.7956 13.9921 14.1920 14.3953 14.6020
13 14.4565 14.2368 14.6803 14.9083 15.1404 15.3769 15.6178 15.8631 16.1130
14 15.7095 15.4504 15.9739 16.2437 16.5190 16.7998 17.0863 17.3787 17.6770
15 16.9844 16.6821 17.2934 17.6092 17.9319 18.2618 18.5989 18.9435 19.2957
16 18.2817 17.9324 18.6393 19.0054 19.3802 19.7640 20.1569 20.5592 20.9710
17 19.6016 19.2014 20.0121 20.4330 20.8647 21.3075 21.7616 22.2273 22.7050
18 20.9446 20.4894 21.4123 21.8928 22.3863 22.8934 23.4144 23.9497 24.4997
19 22.3112 21.7967 22.8406 23.3853 23.9460 24.5230 25.1169 25.7281 26.3572
20 23.7016 23.1237 24.2974 24.9115 25.5447 26.1974 26.8704 27.5642 28.2797
Periods* 3.75% 4% 4.5% 5% 6% 7% 8% 9% 10%
1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
2 2.0375 2.0400 2.0450 2.0500 2.0600 2.0700 2.0800 2.0900 2.1000
3 3.1139 3.1216 3.1370 3.1525 3.1836 3.2149 3.2464 3.2781 3.3100
4 4.2307 4.2465 4.2782 4.3101 4.3746 4.4399 4.5061 4.5731 4.6410
5 5.3893 5.4163 5.4707 5.5256 5.6371 5.7507 5.8666 5.9847 6.1051
6 6.5914 6.6330 6.7169 6.8019 6.9753 7.1533 7.3359 7.5233 7.7156
7 7.8386 7.8983 8.0192 8.1420 8.3938 8.6540 8.9228 9.2004 9.4872
8 9.1326 9.2142 9.3800 9.5491 9.8975 10.2598 10.6366 11.0285 11.4359
9 10.4750 10.5828 10.8021 11.0266 11.4913 11.9780 12.4876 13.0210 13.5795
10 11.8678 12.0061 12.2882 12.5779 13.1808 13.8164 14.4866 15.1929 15.9374
11 13.3129 13.4864 13.8412 14.2068 14.9716 15.7836 16.6455 17.5603 18.5312
12 14.8121 15.0258 15.4640 15.9171 16.8699 17.8885 18.9771 20.1407 21.3843
13 16.3676 16.6268 17.1599 17.7130 18.8821 20.1406 21.4953 22.9534 24.5227
14 17.9814 18.2919 18.9321 19.5986 21.0151 22.5505 24.2149 26.0192 27.9750
15 19.6557 20.0236 20.7841 21.5786 23.2760 25.1290 27.1521 29.3609 31.7725
16 21.3927 21.8245 22.7193 23.6575 25.6725 27.8881 30.3243 33.0034 35.9497
17 23.1950 23.6975 24.7417 25.8404 28.2129 30.8402 33.7502 36.9737 40.5447
18 25.0648 25.6454 26.8551 28.1324 30.9057 33.9990 37.4502 41.3013 45.5992
19 27.0047 27.6712 29.0636 30.5390 33.7600 37.3790 41.4463 46.0185 51.1591
20 29.0174 29.7781 31.3714 33.0660 36.7856 40.9955 45.7620 51.1601 57.2750
*There is one payment each period.
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