Question

A loan is being repaid with level annual payments based on an annual effective interest rate of 8%. If the amount of principal repaid in the 15th payment is 749.63, calculate the amount of principal repaid in the 7th payment. (A) 375 (B) 405 (C) 437 (D) 472 (E) 510

Answer 1

Answer:

option (B) 405

Step-by-step explanation:

Data provided in the question:

Annual effective interest rate, r = 8%

Amount of principal repaid in the 15th payment = 749.63

Now,

Under level annual payment,

Principal portion grow by effective interest

Therefore,

$P_t=P_n\times(1+r)^{t-n}$

Here,

$P_t$ is the principal portion of the $t^{th}$ payment

thus,

P₇ = P₁₅ × ( 1 + 0.08 )⁽⁷⁻¹⁵⁾

or

P₇ = 749.63 × ( 1.08 )⁻⁸

or

P₇ = 405.00

Hence,

the correct answer is option (B) 405