Question

If $300 is invested at a rate of 5% per year and is compounded quarterly, how much will the investment be worth in 15 years?

Use the compound interest formula A equals P times the quantity 1 plus r divided by n end quantity raised to the power of n times t.

$141.04
$361.45
$515.28
$632.15

Answer 1

Answer:

$632.15

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 = $300
• r = 5% = 0.05
• n = 4 (quarterly)
• t = 15 years

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

$\implies \sf A=300\left(1+\frac{0.05}{4}\right)^{4 \times 15}$

$\implies \sf A=300\left(1.0125}\right)^{60}$

$\implies \sf A=632.1544041$

Therefore, the investment will be worth $632.15 in 15 years.