Question

To repay a loan of $20,000, a series of nineteen level payments is to be made with the first payment in one year and each subsequent payment two years after the preceding one. The annual effective interest rate is 3.5%. Find the payment amount.

A $1,459
B $1,685
C $1,729
D $1,887
E $1.953

Answer 1

The student's question involves calculating the payment amount for a loan repayment using the present value of geometrically increasing annuity formula, considering the time intervals between payments and annual interest rate.

Step-by-step explanation:

The subject student is trying to calculate the level payment amount for a loan repayment using the concept of a geometric series to account for the increasing time intervals between payments. To find the payment amount, we need to consider that each payment is made two years after the previous one, leading to a decreasing present value for the later payments due to the effect of interest compounded annually.

The student must use the formula for the present value of a geometrically increasing annuity to identify the regular payment required to repay a $20,000 loan over nineteen payments with an annual effective interest rate of 3.5%. An illustration of similar calculations can be found in the situation where someone makes regular payments on a bigger loan, such as a $1,000,000 house loan over 30 years at a nominal interest rate.