Question

# Andrew borrowed \$7,000 at 5% interest compounded annually for 3 years. He did not need to...

Andrew borrowed \$7,000 at 5% interest compounded annually for 3 years. He did not need to make payments but instead would repay the entire loan with interest at the end of 3 years. Being a responsible bloke, Andrew decided to set up a sinking fund to ensure he had the money ready to repay this loan. On the day Andrew borrowed money he also found a bank offering 4% interest compounded quarterly. How much must he deposit at the end of each quarter to ensure he has enough money to repay the loan.

First let us calculate the amount the Andrew had to pay back after 3 years

For compound Interest

A = P(1+(r/100))^n

= 7000(1+0.05)^3

= \$8103.375

4% interest compounded quarterly Interest rate every quarter =4/4 = 1%

There are a total of 12 quarters in 3 years

Since he deposits it at the end of every quarter, there will be 11 deposits earning him income

Let amount deposited each quarter = x

Therefore total value of deposits = x(1.04^11) + x(1.04^10) + x(1.04^9) + ..... +x = 8103.375

x[(1.04^12)-1]/(1.04-1) = 8103.375

x(0.601)/0.04 = 8103.375

x= \$ 539.33

Therefore Andrew must deposit \$539.33 every quarter to ensure he has money to pay the loan