Question

Toby is borrowing $500,000 to buy a house, and he will repay this loan with 25 equal yearly payments starting one year from today. If the effective annual interest rate is 14%, what is the dollar amount of each yearly payment?

Toby is borrowing $500,000 to buy a house, and he will repay this loan with 25 equal yearly payments starting one year from today. If the effective annual interest rate is 14%, what is the dollar amount of each yearly payment? Select one: o a. $75,890 o b. $72,749 c. $50,877 d. $62,900 o e. $60,344

I don't know how to do this, please help. I don't JUST want the answer, I want an expalanation on how to do the problem and eventually get the answer myself.

Thank you

Answer 1

This question requires application of PV of annuity formula, according to which

PV =

[1-(4+5)-) [1-(1+r)-n LT P= Periodic Payment r=rate per period n = number of periods

For this question,

$500,000 = P * [\frac{1-(1 + 0.14)^{-25}}{0.14}]$

500,000 = P * 6.872927

P = $72,749.20 (Option B)