Question

8. Claude made semi- annual deposits of $ 3100 at the beginning of a six- month period into a fund earning 6.8% compounded semi- annually for nine years. No further deposits were made.

( a) How much will be in the account 15 years after the first deposit? ( b) How much in total was deposited? ( c) How much interest will have been earned?

Answer 1

How much will be in the account 15 years after the first deposit?

Because no deposits are made after nine years the amount in the account after 15 years will be the same as after nine years FV= ? m = 9 I = 0.068/2 = 0.034 n = 9x2= 18 PMT = 3100

FV= 3100(1.034^18 – 1 / 0.034)(1.034)

FV = 3100(1.82544897331 – 1 / 0.034)(1.034)

FV = 3100(0.82544897331/0.034)(1.034)

FV = 3100(24.2779109798)(1.034)

FV = 77820.4158546

The account will have $77,820.42 after 15 years.

b. how much in total was deposited?

Total deposits = PMT x 9 years x 2(semi-annual)

= 3100(9)(2)

= 55800

The total deposited was $55,800.

c. How much interest will have been earned?

Interest earned = accumulated value – total deposit= 77820.4158546 – 55800 = 22020.42

Total interest earned was $22,020.42.

Thanks