Question

If a farmer is granted a loan for $3,000, with a 6 years of fully amortized monthly payments of $75. What is actuarial rate?

A. 2.63%

B. 4.26%

C. 1.82%

D. None of the answers are correct

Answer 1

Ans: 1.82%

Explanation:

Here, P = 3000,

A = 75

n = 6 * 12 = 72

A = P(A/P, i, n)

75 =3000(A/P, i, 72)

(A/P, i, 72) = 75 / 3000 = 0.025

From the interest table we found that the value of (A/P, i, 72) at 1% is 0.0195 and at 2% it is 0.0263. It means 0.025 lies in between 1% and 2%.

By interpolation,

i = 1% + [(0.0195 - 0.025) / (0.0195 - 0.0262)] * (2% - 1%)

= 0.01 + (-0.0055 / -0.0068) * 0.01

= 0.01 + 0.0082

= 0.0182 or 1.81%