Question

A debt payment that was due 18 months ago will instead be repaid with an equivalent value of $940.36 in 14 months from now. The interest rate is 9.49% compounded monthly.

a) What value of N should be used for calculations?

b) What was the original value of the debt payment?

Answer 1

To find the value of N, we can use the formula for compound interest. The original value of the debt payment is approximately $879.74.

Step-by-step explanation:

To solve this problem, we can use the formula for compound interest, which is: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per time period, and t is the time period in years.

a) To find the value of N, we can rearrange the formula to solve for N: N = (log(A/P))/(log(1 + r/n)^t). Substituting the given values, we get N ≈ 18.437 months. Since N represents the number of months, we round up to the nearest integer, which is 19.

b) To find the original value of the debt payment, we can use the formula: P = A/(1 + r/n)^(nt). Substituting the given values, we get P ≈ $879.74.