Question

Consider an investment of $6000 that earns 4.5% interest

What is the value of the investment after
15 years if the interest is compounded
annually?

Answer 1

$11,611.69

Explanation:

Compound Interest Formula

`\large \text{$ \sf A=P\left(1+(r)/(n)\right)^(nt) $}`

where:

• A = final amount
• P = principal amount
• r = interest rate (in decimal form)
• n = number of times interest applied per time period
• t = number of time periods elapsed

Given:

• P = $6,000
• r = 4.5% = 0.045
• n = 1 (annually)
• t = 15 years

Substitute the given values into the formula and solve for A:

`\implies \sf A=6000\left(1+(0.045)/(1)\right)^((1 * 15))`

`\implies \sf A=6000(1.045)^(15)`

`\implies \sf A=11611.69466...`

Therefore, the value of the investment after 15 years will be $11,611.69 to the nearest cent.