Question

Mr. Dawson wants to receive payments of $1,320.00 at the beginning of every month for 19 years starting on the date of the retirement. If he retires in 21 years, how much must he deposit in an account at the beginning of every month if interest on the account is 6.84% compounded monthly?

A. $222.41

B. $242.81

C. $228.81

D. $280.21

E. $284.21

Answer 1

After Retirement,

Monthly Requirement(beginning) = $1,320

Time Period = 19 years

Calculating Present Value,

Present Value of Annuity = P + P[(1 - (1 + r)^{-(n - 1)})/r]

Present Value = 1320 + 1320[((1 - 1.0684)^-227)/(0.0684/12)]

Present Value = $169,166.46

Using Present Value as Future Accumulated Value,

Time Period = 21 years = 252 months

Future Value = $169,166.46

Interest Rate = 6.84%

Calculating Beginning Monthly Deposit,

Future Value of Annuity Due = (1 + r)P[((1 + r)ⁿ - 1)/r]

169,166.46 = (1 + 0.0684/12)P[(1 + 0.0684/12)²⁵² - 1)/(0.0684/12)]

P = $284.21