1.Mr. Clark made deposits of $950 at the end of every 6 months for 15 years....

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?

Solutions

Expert Solution

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

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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

keosha answered 1 year ago

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