Question

Brent Pickett borrowed $2000 from his brother Dave. He agreed to repay the money ate the end of three years, giving Dave the same amount of interest that he would have received if the money had been invested at 2.75% compounded quarterly. How much money did Brent repay his brother

Answer 1

Hello there. To solve this question, we'll have to remember some properties about investments.

Knowing Brent borrowed $2000 from his brother and will pay him the same amount of interest that he would have received if the money had been invested at 2.75% compounded quarterly, we need to find how much money will Brent repay his brother.

First, we have to remember the formula to find the amount a principal value P will become after t years, invested at an interesting rate r, compounded quarterly.

It is given by:

`A=P\cdot\mleft(1+(r)/(4)\mright)^(4t)`

Plugging in P = 2000, r = 2.75% (converted in decimals, divide by 100) and t = 3, we get:

`A=2000\cdot\mleft(1+(0.0275)/(4)\mright)^(4\cdot3)=2000\cdot\mleft(1+0.006875\mright)^(12)`

Add the values inside parenthesis and calculate the power (with the help of a calculator)

`A=2000\cdot1.006875^(12)\approx2000\cdot1.0857=2171.38`

This is the amount Brent had to repay his brother.