Question

A loan is being amortized by means of level monthly payments at an annual effective interest rate of 8%. The amount of principal repaid in the 12th payment is 1000 and the amount of principal repaid in the tth payment is 3700. Calculate t.

Answer 1

Option D. 216

Step-by-step explanation:

The value of "t" can be calculated using the compounding formula given as under:

Principal Amount * (1 + r)^(t-n)/n = Future Value

Here

Principal Amount is $1,000

r is 8%

n is the number of payment which is 12th here

Future Value is $3,700

By putting values, we have:

$1,000 * (1 + 8%)^(t-12)/12 = $3,700

(1.08)^ (t-12)/12 = 3.7

By taking natural log on both sides:

(t-12)/12 = 17

t = 216