Question

Will the account balance be aller 17 years!

3) Ashley invests $4,650 in a savings
account with a fixed annual interest rate of
9% compounded 12 times per year. What
will the account balance be after 12 years?

Answer 1

Account balance after 17 years: $21,352.27

Explanation:

Use the formula for amount after compound interest.

A = P(1+i)ⁿ

What the variables mean:

"A" is for amount after the time period.

"P" is principal, meaning starting money.

"i" is the interest per compounding period.

"n" is the total number of compounding periods.

"c" is the compounding periods each year. (annual = 1; monthly = 12, etc)

To calculate "i":

i = r/c

"r" is the annual interest rate in decimal form.

To calculate "n":

n = t*c

"t" is the time, usually the number of years.

Now can combine these formulas:

`A = P(1+(r)/(c))^(t*c)`

What do we know from the problem?

t = 17 years

P = 4650

r = 9% = 0.09

c = 12

Substitute them into the formula.

`A = P(1+(r)/(c))^(t*c)`

`A = 4650(1+(0.09)/(12))^(17*12)` Simplify

`A = 4650(1.0075)^(204)` Do the exponent with a calculator

`A = 4650(4.59188689)` Multiply

`A = 21352.274` Unrounded answer

A ≈ 21352.27 Round down because "4" is less than 5.

Therefore Ashley's account balance after 17 years will be $21,352.27.