# If you borrow $500,000 to buy a luxury yacht and the mortgage calls for payments of$120,022.08...

## Question:

If you borrow $500,000 to buy a luxury yacht and the mortgage calls for payments of$120,022.08 for each of the next 40 years, what rate of interest are you paying, assuming annual compounding?

## Mortgage and Amortization:

A mortgage is a loan with a real estate as collateral. Mortgages are often amortized over a long period of time, which implies that loan is repaid through periodic payments over the amortization period.

## Answer and Explanation:

The annual interest rate is 24%.

We can use the following formula to compute the annual payment for a loan with principal {eq}P {/eq}, annual interest rate {eq}r{/eq} and number of annual payments {eq}T{/eq}:

• {eq}\displaystyle \frac{Pr}{1 - (1 + r)^{-T}} {/eq}

In this question, the amount borrowed is 500,000, annual payment is 12,022.08, and there are 40 payments. Applying the formula, we have:

• {eq}\displaystyle \frac{120,022.08*r}{1 - (1 + r)^{-40}} = 500,000 {/eq}

which yields:

• {eq}r = 24\% {/eq}

#### Learn more about this topic: Calculating Monthly Loan Payments

from Remedial Algebra I

Chapter 25 / Lesson 8
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