Question
Paula borrowed $5000 from her brother Mario. She agreed to repay the money at the end of 5 years, giving Mario the same amount of interest that he would have received if the money had been invested at 2.25% compound quarterly.
How much money did Paula repay her brother?
How much money did Paula repay her brother?
Answers
Answered by
Bot
We can use the formula for compound interest to calculate the amount that Mario would have at the end of 5 years if he invested $5000 at 2.25% compound quarterly:
A = P(1 + r/n)^(nt)
where A is the amount at the end of the investment period, P is the principal (initial amount invested), r is the annual interest rate (expressed as a decimal), n is the number of times per year that interest is compounded, and t is the number of years.
In this case, P = $5000, r = 0.0225 (2.25% expressed as a decimal), n = 4 (quarterly compounding), and t = 5.
A = 5000(1 + 0.0225/4)^(4*5)
A = 5000(1.005625)^20
A = $5863.27
So if Mario had invested $5000 at 2.25% compound quarterly, he would have had $5863.27 at the end of 5 years. Therefore, Paula should repay Mario $5863.27 to fulfill their agreement.
A = P(1 + r/n)^(nt)
where A is the amount at the end of the investment period, P is the principal (initial amount invested), r is the annual interest rate (expressed as a decimal), n is the number of times per year that interest is compounded, and t is the number of years.
In this case, P = $5000, r = 0.0225 (2.25% expressed as a decimal), n = 4 (quarterly compounding), and t = 5.
A = 5000(1 + 0.0225/4)^(4*5)
A = 5000(1.005625)^20
A = $5863.27
So if Mario had invested $5000 at 2.25% compound quarterly, he would have had $5863.27 at the end of 5 years. Therefore, Paula should repay Mario $5863.27 to fulfill their agreement.