Final answer:
To calculate the student's monthly loan payment, the formula for a monthly compounded interest loan was applied, using the given loan amount of $13,000, annual interest of 3.68%, and a term of 5 years. The closest approximate monthly payment is $225.55, which is not an exact match to any of the provided options, but option a) $237.50 is the closest.
Step-by-step explanation:
The student's question pertains to finding the monthly payment of a 5-year loan of $13,000 with a 3.68% annual interest rate, compounded monthly. To answer this question, we need to use the formula for calculating the monthly payment of a compound interest loan, which is:
PMT = P * (r/n) / [1 - (1 + r/n)^(-nt)]
Where:
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- PMT is the monthly payment
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- P is the principal amount ($13,000)
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- r is the annual interest rate (0.0368)
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- n is the number of times that interest is compounded per year (12)
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- t is the number of years the money is borrowed for (5)
Plugging in the values we get:
PMT = 13000 * (0.0368/12) / [1 - (1 + 0.0368/12)^(-12*5)]
Calculating this gives us:
PMT = 13000 * 0.00306667 / [1 - (1 + 0.00306667)^(-60)]
PMT = 39.86671 / [1 - (1 + 0.00306667)^(-60)]
PMT = 39.86671 / (1 - 0.82319091)
PMT = 39.86671 / 0.17680909
PMT = $225.54531
Therefore, the monthly payment Priya needs to make on her loan is approximately $225.55, which is not one of the options provided. It's important to note that the formula assumes exact mathematical calculations and actual bank calculations might differ slightly due to rounding or other factors. If an option must be chosen, the closest match would be $237.50.