Question

Answers currently posted for this question are incorrect. Today you opened up a local bank account. Your plan is to make five $4,000 contributions to this account. The first $4,000 contribution will occur today and then every six months you will contribute another $4,000 to the account. (So your final $4,000 contribution will be made two years from today). The bank account pays a 6% APR that is compounded monthly. After two years, you plan to leave the money in the account earning interest, but you will not make any further contributions to the account. How much will you have in the account 6 years from today?

Answer 1

first we have to find effective annual rate for 6 months

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

where r = APR

n = compounding periods

(1 + (6%/12))^12 - 1 = (1 + r)^2 - 1

r = 3.038%

future value of annuity = P*[(1+r)^n - 1 / r ]*(1+r)

where P = periodic payments

r = rate per period

n = number of periods

= 4000*[(1+3.038%)^4 - 1 / 3.038%]*(1+3.038%)

=17252.58

value after 5th payment = 17252.58+4000

= 21,252.58

future value = present value*(1+r)^n

= 21,252.58*(1+0.5%)^48

= 27,001.17

value 6 years from today = $27,001.17