Question

# You are planning to make monthly deposits of \$160 into a retirement account that pays 12...

You are planning to make monthly deposits of \$160 into a retirement account that pays 12 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement account be in 24 years?

A. \$278,229.15

B. \$251,731.14

C. \$226,858.06

D. \$264,980.14

E. \$3,179,761.74

 Annual rate= 12% Monthly rate = 12/12 = 1% Monthly deposits 160 Multiply: Annuity FVF at 1% for 288 periods 1656.126 Amount in account at the end of 24 years 264980.1 Answr is d. 264980.14

SOLUTION :

Monthly compounding.

Monthly deposit, A = 160 (\$) starting from next month.

Monthly interest rate, r = 12/12 =1% = 0.01 in decimals

=> 1 = r = 1.01

Periods, n = 24 * 12 = 288 months

So,

FV after 24 years (288 months)

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

= 160 * (1.01^288 - 1) / 0.01

= 264980.14 (\$)

So, ANSWER is OPTION D : \$264,980.14

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