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

Answer:

$15,539.67

Step-by-step explanation:

Compound Interest Formula

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

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:

$\implies \sf A=11000\left(1+\frac{0.058}{4}\right)^{(4 \times 6)}$

$\implies \sf A=11000(1.0145)^{24}$

$\implies \sf A=15539.67451...$

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