You borrow $10,000 at an interest rate of 6% per year compounded monthly. You ma

Question

You borrow $10,000 at an interest rate of 6% per year compounded monthly. You make 24 monthly payments for 2 years, with the value of the 12 uniform monthly payments in the first year changing in the second year by being doubled in value for the remaining 12 uniform monthly payments made in the second year. What is the monthly payment amount during the first year and the monthly payment amount during the second year?

Evaluate the loan payment amounts of this loan. Select the appropriate theoretical interest factor notation equation you will use to calculate the two loan payment values and first set up the interest factor notation equation to solve the problem, next either calculate the required interest factor values from their respective algebraic formulas or obtain them from the appropriate interest factor table. Then substitute the given information and interest factor values into the interest factor equation and solve equation for the unknown payment amounts. Clearly show all steps in your sequence of calculations.

Explanation / Answer

Amount = $10,000. Compounding is done monthly so the effective rate will be = (1+r/12)^12 = (1+6%/12)^12 = 1.0617. Thus the effective annual rate = 1.0617 -1 = 0.0617 or 6.17%

Now, future value or the amount at the end of 2 years = 10,000*(1+0.0617)^2 = 11,271.5978

Let the monthly payments being made in the 1st year be = x. The total amount being paid = 12*x = 12x.

This amount is doubled in 2nd year. Thus monthly payment of x will be doubled to 2x. Total amount paid in 2nd year = 2x*12 = 24x. Total payment of 1st and 2nd year = 12x+24x = 36x

Now, 36x = 11,271.5978

or x = 11,271.5978 = $313.0999. This is the monthly payment being made during the 1st year.

Monthly payments for 2nd year = 2x = 2*313.0999 = $626.1999

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