Question

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.

Answer 1

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