Question

Use the periodic compound interest formula to solve.

Suppose that $11,000 is invested at 5.8% compounded quarterly. Find the total amount of this investment after 6 years.

Answer 1

$15,539.67

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 = $11,000
• r = 5.8% = 0.058
• n = 4 (quarterly)
• t = 6 years

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

`\implies \sf A=11000\left(1+(0.058)/(4)\right)^((4 * 6))`

`\implies \sf A=11000(1.0145)^(24)`

`\implies \sf A=15539.67451...`

Therefore, the value of the investment after 6 years will be $15,539.67 to the nearest cent.