Question

Present and future value tables of $1 at 3% are presented below:
N FV $1 PV $1 FVA $1 PVA $1 FVAD $1 PVAD $1
1 1.03000 0.97087 1.0000 0.97087 1.0300 1.00000
2 1.06090 0.94260 2.0300 1.91347 2.0909 1.97087
3 1.09273 0.91514 3.0909 2.82861 3.1836 2.91347
4 1.12551 0.88849 4.1836 3.71710 4.3091 3.82861
5 1.15927 0.86261 5.3091 4.57971 5.4684 4.71710
6 1.19405 0.83748 6.4684 5.41719 6.6625 5.57971
7 1.22987 0.81309 7.6625 6.23028 7.8923 6.41719
8 1.26677 0.78941 8.8923 7.01969 9.1591 7.23028
9 1.30477 0.76642 10.1591 7.78611 10.4639 8.01969
10 1.34392 0.74409 11.4639 8.53020 11.8078 8.78611
11 1.38423 0.72242 12.8078 9.25262 13.1920 9.53020
12 1.42576 0.70138 14.1920 9.95400 14.6178 10.25262
13 1.46853 0.68095 15.6178 10.63496 16.0863 10.95400
14 1.51259 0.66112 17.0863 11.29607 17.5989 11.63496
15 1.55797 0.64186 18.5989 11.93794 19.1569 12.29607
16 1.60471 0.62317 20.1569 12.56110 20.7616 12.93794
At the end of each quarter, Patti deposits $2,200 into an account that pays 12% interest compounded quarterly. How much will Patti have in the account in 4 years?
a. $31,060.
b. $29,551.
c. $30,532.
d. $29,803.

Answer 1

Based on the amount being deposited, Patti will have a total of $44,345.18 after 4 years.

Patti is depositing a specific amount every month so this is an annuity.

First we have to convert the interest rate and period to quarterly basis as this is the period of compounding.

12%/4 = 3% per quarter

Period = 4 x 4 = 16 quarters

The value of this investment after 4 years is:

Future value of Annuity = Annuity x FVA,16 periods, 3%

= 2,200 x 20.1569

= $44,345.18

In conclusion, Patti will have $44,345.18 in 4 years.

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