Question

An amount of 24,000 is borrowed for 14 years at 6% interest compound annually. If the loan is paid in full at the end of the period how much must be paid? Round your answer to the nearest dollar

Answer 1

To solve this problem, we must use the Compound Interest formula:

`P_N=P_0\cdot(1+(r)/(k))^(N\cdot k).`

Where:

• P_N is the balance in the account after N years,

,

• P_0 is the starting balance of the account (also called an initial deposit, or principal),

,

• r is the annual interest rate in decimal form,

,

• k is the number of compounding periods in one year.

In this problem, we have:

• P_0 = 24,000,

,

• r = 6% = 0.06%,

,

• k = 1 (because the interest compounded annually),

,

• N = 14.

Replacing the data in the equation above, we get:

`P_(14)=24,000\cdot(1+0.06)^(14)\cong54,261.6944\cong54,262.`

Answer

The amount to be paid at the end of the 14 years will be $54,262.