Question

What would the monthly payment be for a $5,000 loan with a 6. 25% interest rate compounded monthly spread over 60 months? a. $25. 31 b. $97. 25 c. $217. 00 d. $320. 95.

Answer 1

Answer:

  b.  $97.25

Step-by-step explanation:

Your number sense tells you a loan of this duration will have a monthly payment not much greater than $5000/60 ≈ $83. Of the offered answer choices, $97.25 is the most reasonable guess.

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If you work this out using a financial calculator, it will tell you the monthly payment is $97.25.

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Additional comment

As a first approximation, the interest paid on an amortized loan is about half of the simple interest amount. We can guess at the monthly payment by computing the payment on a simple interest loan at half the rate.

The total due on a $5000 loan at 3.125% interest is ...

  A = P(1 +rt) = 5000(1 +5(0.03125)) = 5000(1.15625) = 5781.25

If 1/60 of that is paid each month, the payment is about $96.35. This guess is within 10% of the actual payment value. With suitable approximations, you can do this calculation without a calculator.