Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

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

Sagot :

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

[tex]P_N=P_0\cdot(1+\frac{r}{k})^{N\cdot k}.[/tex]

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:

[tex]P_{14}=24,000\cdot(1+0.06)^{14}\cong54,261.6944\cong54,262.[/tex]

Answer

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