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Answer:
a) $608.05
c) $72,966
e) $11,766
g) $19,935
Step-by-step explanation:
The formula for the monthly payment amount on a loan of P at rate r for t years is ...
A = P(r/12)/(1 -(1 +r/12)^(-12t))
For the standard repayment plan, t = 10. You have P = $61,200 and r = 0.036, so the formula becomes ...
A = $61,200(0.036/12)/(1 -(1 +0.036/12)^(-12·10))
= $61,200(0.003)/(1 -1.003^-120)
= $608.05
a) The monthly payment under the standard repayment plan is $608.05.
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c) The total of 12 payments per year over 10 years is ...
$608.05×10×12 = $72,966.00
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e) The interest paid is the difference between payments and the amount borrowed:
interest = $72,966 -61,200 = $11,766
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g) Payments under the extended repayment plan last for 25 years (300 months). They will be $309.67 (found using a financial calculator). The total of those payments will be $309.67×300 = $92,901. Your savings under the standard plan are ...
$92,901 -72,966 = $19,935
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Additional comment
Many graphing calculators have apps for figuring loan payments or other parameters. Spreadsheets have these functions, too.
Here, we have rounded the loan payment value to the nearest cent. This means the payment differs slightly from the computed value. In the real world, the final loan payment will be different from the rest, so as to take care of this discrepancy. In addition to the unpaid principal, there will be an interest charge that depends on the precise day on which the final payment is made.
We're never quite sure how accurate the answer is expected to be, so we've done the calculations using the loan payment value we came up with.
