Question

Brent Pickett borrowed 3000 from his brother Dave. He agreed to repay the money at the end of 4 years giving Dave the same amount of interest that he would have received if the money had been invested at 1.75% compound quarterly. How much did Brent repay his brother?

Answer 1

Brent Pickett would repay his brother Dave approximately $3217.15 after borrowing $3000 at an interest rate of 1.75% compounded quarterly over 4 years.

Step-by-step explanation:

The student has asked how much Brent would repay his brother Dave after borrowing $3000 and agreeing to repay it at the end of 4 years with interest compounded quarterly at a rate of 1.75%. To calculate this, we use the formula for compound interest which is:

A = P(1 + r/n)(nt)

Where:

A = the amount of money accumulated after n years, including interest.

P = the principal amount (the initial amount of money).

r = the annual interest rate (decimal).

n = the number of times that interest is compounded per year.

t = the time the money is invested or borrowed for, in years.

Substituting the given values into the formula, we get:

A = $3000(1 + 0.0175/4)(4*4)

Calculating this gives us the total amount that Brent would repay to Dave:

A = $3000(1 + 0.004375)16

A = $3000(1.004375)16

A ≈ $3000(1.072384)

A ≈ $3217.15

Hence, Brent would repay Dave approximately $3217.15 after 4 years.