A loan is repaid at the rate of $200 per week for 15 years. if the interest rate is 6.65% per annum.Calculate the the total amount repaid
i = weekly rate = .0665/52 = .001278846
n = number of payments = 52(15) = 780
Amount repaid = present value of loan
= 200( 1 - 1.001278846^-780)/.001278846
= appr $98,677.00
Why is it present value
To calculate the total amount repaid on a loan, you need to consider both the principal amount borrowed and the interest accrued over the repayment period.
First, let's calculate the total number of weeks over the 15-year repayment period:
15 years * 52 weeks/year = 780 weeks
Next, let's calculate the total principal amount borrowed over the repayment period:
$200/week * 780 weeks = $156,000
Now, let's calculate the total interest accrued over the repayment period. We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Total amount repaid
P = Principal amount borrowed
r = Annual interest rate (as a decimal)
n = Number of times interest applied per year
t = Number of years
In this case, the annual interest rate is 6.65% or 0.0665 as a decimal. The interest is compounded annually, so n = 1.
Using these values, the formula becomes:
A = $156,000(1 + 0.0665/1)^(1*15)
Now, let's calculate the total amount repaid:
A = $156,000(1 + 0.0665)^15
A = $156,000(1.0665)^15
A ≈ $472,305.72
Therefore, the total amount repaid on the loan is approximately $472,305.72.