Question

On September 8, Bert Sarkis started an annuity. He arranged to have $65 deducted from his end-of-month paychecks. The money would earn 6% interest compounded monthly.

A.) Find the future value of the account on December 1 using an Amortization Formula. (Round your answer to the nearest cent.)    

B.) Find the future value of the account on December 1 by applying the Compound Interest Formula to each payment individually. (Round your answer to the nearest cent.)

C.) Find Bert's total contribution to the account.    

D.) Find the total interest. (Round your answer to the nearest cent.)    

Answer 1

Since the paychecks are end of the month, the first contribution will come at the end of Sept

2nd contribution end of October

3rd contribution at the end of November

Rate is 6% per annum therefore 6%/12 = 0.005 per month

A)

Amortization means the process of reducing the value of an asset or the balance of a loan by a periodic amount. But in the above case there is a contribution not towards a loan but towards an interest earning account.

Hence it is a case of ordinary annuity

Future value of Ordinary Annuity formula

annuities* (((1+i)^n)-1) / i

65 * ((1+0.005)^3) -1) / 0.005)

(65 * (0.02/3.015025))

195.976625

B) Future value compound interest formula

at the end of October

(Sept contribution) 65*1.005 + 65 (Oct contribution)

130.325

At the end of November

(130.325 * 1.005) + 65

195.976625

C) Total contribution = 65 *3 = 195

D) Interest = Total future value - Total contribution

195.98-195 = 0.98