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You are planning to make monthly deposits of $120 into a retirement account that pays 13...

You are planning to make monthly deposits of $120 into a retirement account that pays 13 percent interest compounded monthly.

You are planning to make monthly deposits of $120 into a retirement account that pays 13 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement account be in 29 years? Multiple Choice $436,806.71 Ο $5,517,558.49 Ο $482,786.37 Ο $372,360.06 Ο $459,796.54
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Answer #1
Future value of investment = Monthly deposit * Future value of annuity of 1
= $           120.00 * 3831.638
= $ 4,59,796.54
Working:
Future value of annuity of 1 = (((1+i)^n)-1)/i Where,
= 3831.637843 i = 13%/12 = 0.010833
n = 29*12 = 348
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Answer #2

SOLUTION :


Monthly compounding.


Monthly deposit, A = 120 ($)


Monthly interest rate, r = 13/12 % = 13/1200 in fractions.

=> 1 + r = 1213/1200 


Periods, n = 29 * 12 = 348 months


So, 


FV after 29 years (348 months)


= A((1 + r)^n - 1) / r

= 120 * ((1213/1200)^348 - 1) / (13/1200)

= 459796.54 ($)  : 5th OPTION (ANSWER).

answered by: Tulsiram Garg
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