Question

Sally invests $10,00o into a new bank account at 8.4% interest compoundedmonthly. How much money will Sally have in the account in 30 years to the nearestcent?

Answer 1

EXPLANATION

The compound interest formula is

$A=P(1+\frac{r}{n})^{nt}$

P= Principal = $10,000

Interest rate = 8.4% = 0.084 in decimal form

n= Number of times interest rate is compounded per unit "t" = 12

t= Time = 30 years

Replacing terms:

$A=10,000(1+\frac{0.084}{12})^{12\cdot30}$

Multiplying and dividing numbers:

$A=10,000(1+0.007)^{360}$

Adding numbers:

$A=10,000\cdot\text{1}.007^{360}$

Solving the power:

$A=10,000\cdot12.32$

Multiplying terms:

$A=\text{ 123,200}$

Sally will have $123,200 in 30 years.