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
To calculate the amount Paula would need to repay at the end of 5 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
where:
A = the amount owed at the end of the 5 years
P = the principal amount borrowed ($5000)
r = the annual interest rate (2.25%)
n = the number of times interest is compounded per year (4 for quarterly)
t = the number of years (5)
Plugging in the values, we get:
A = 5000(1 + 0.0225/4)^(4 x 5)
A = 5000(1.005625)^20
A = 5000(1.122078)
A = $5,610.39
Therefore, Paula would need to repay $5,610.39 to her brother Mario at the end of 5 years, including the interest of 2.25% compounded quarterly.
To calculate the compound interest and the total repayment amount, we need to use the following formula:
A = P(1 + r/n)^(nt)
Where:
A = Total repayment amount
P = Principal (initial borrowed amount)
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
Given:
P = $5000
r = 2.25% (in decimal form, 0.0225)
n = 4 (quarterly compounding)
t = 5 years
Let's calculate the total repayment amount (A):
A = 5000(1 + 0.0225/4)^(4*5)
A = 5000(1 + 0.005625)^(20)
A = 5000(1.005625)^(20)
A ≈ 5000(1.11990326069)
A ≈ $5599.52
Therefore, Paula needs to repay Mario approximately $5599.52 at the end of 5 years to give him the same amount of interest he would have received if the money had been invested at 2.25% compound quarterly.