Karen obtained a $36,000 loan at 3.5% compounded semiannually.a-1. What monthly payment will repay the loan in 8 1/2 years? (Do not round intermediate calculations and round your final answer to 2 decimal places.)Monthly payment $ a-2. How much interest will Karen pay over the life of the loan? (Round intermediate calculations to 2 decimal places and round your final answer to the nearest dollar.)Total interest $
Question
Karen obtained a a-2. How much interest will Karen pay over the life of the loan? (Round intermediate calculations to 2 decimal places and round your final answer to the nearest dollar.)Total interest $
Solution
a-1. To calculate the monthly payment, we first need to find the semiannual interest rate and the number of periods.
The semiannual interest rate is 3.5% / 2 = 1.75% or 0.0175 in decimal form.
The number of periods is 8.5 years * 2 = 17 periods.
We can use the formula for the payment of an ordinary annuity:
PMT = PV * r * (1 + r)^n / [(1 + r)^n - 1]
where: PMT = payment PV = present value or loan amount r = semiannual interest rate n = number of periods
Substituting the values we have:
PMT = $36,000 * 0.0175 * (1 + 0.0175)^17 / [(1 + 0.0175)^17 - 1]
Calculating this gives us a semiannual payment of approximately $2,725.97.
However, we need to find the monthly payment. Since there are 6 months in a semiannual period, we divide the semiannual payment by 6:
Monthly payment = 454.33
a-2. To find the total interest paid over the life of the loan, we first find the total payment over the life of the loan, and then subtract the original loan amount.
Total payment = monthly payment * number of months Total payment = 46,239.78
Total interest = total payment - loan amount Total interest = 36,000 = $10,239.78
So, Karen will pay approximately $10,240 in interest over the life of the loan.
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