Question

Suppose that when your friend was born, your friend's parents deposited $9000 in an account paying %6.6 interest compounded . What will the account balance be after 13 years

Answer 1

We are given the following information

Deposited amount = P = $9000

Interest rate = r = 6.6% = 0.066

Compounding interval = n = quarterly = 4

Number of years = t = 13

We are asked to find the accumulated amount (or ending balance)

Recall that the compound interest formula is given by

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

Where

A = Accumulated amount (or ending balance)

P = Deposit amount

r = Interest rate in decimal

n = Number of compounding in a year

t = Number of years

Now let us substitute the given values into the above formula

$\begin{gathered} A=P(1+\frac{r}{n})^{n\cdot t} \\ A=9000\cdot(1+\frac{0.066}{4})^{4\cdot13} \\ A=9000\cdot(1+0.0165)^{52} \\ A=9000\cdot(1.0165)^{52} \\ A=\ 21077.85 \end{gathered}$

Therefore, after 13 years, the account balance will be $21077.85