Question

1.Mr. Clark made deposits of $950 at the end of every 6 months for 15 years. If interest is 3% compounded monthly and if he leaves the accumulated balance for another 10 years, what will be the balance in his account then? (i.e. 10 years after the last deposit)   _______________

How much of the accumulated amount is interest?

2.Amy borrowed $6,200 to buy a car to drive to school. She plans to study for three years, and then start her career using her education. Interest is charged on the loan at 7.64% compounded annually. If start making month-end payments of $230 when she begins working, how many payments will she have to make?

Answer 1

1)

The payment frequency and compounding frequency are not the same. The payment is made semi-annually whereas the compounding is made monthly. Hence, we have to find the semi-annual interest rate.

The value of the deposit at the end of 15 years is found using future value of annuity equation

Value of deposit after 15 years =  $35,713.39

Balance in the account 10 years after the last deposit is found as follows

Balance in the account 10 years after the last deposit =  $48,189.99 $ 48,190

---------------------------------------------------------------------------------------------------------------------------

2)

The number of payments she will have to make is found using the following equation

Solving for t in the above equation

t = 2.47 years or 29.67 months

The number of payments she will have to make =  2.47 years or 29.67 months