Question

Harry just deposited $1500 into a savings account giving 6% interest compounded monthly. How much will be in the account after 10 years and 20 years ?

Answer 1

Compound Interest

It occurs when the interest is reinvested rather than paying it out.

When it happens interest in the next period is then earned on the principal sum plus previously accumulated interest.

The formula is:

`{\displaystyle A=P\mleft(1+{(r)/(n)}\mright)^(nt)}`

Where:

A=final amount

P=initial principal balance

r=interest rate

n=number of times interest applied per time period

t=number of time periods elapsed

Harry deposited an initial amount of P = $1500.

The savings account gives r = 6% = 0.06 interest

Since the interest is compounded monthly, n = 12 (there are 12 months in a year)

The time is t = 10 years.

Now we apply the formula:

`\begin{gathered} {\displaystyle A=1500(1+{(0.06)/(12)})^(12\cdot10)} \\ \text{Calculating:} \\ {\displaystyle A=1500(1+0.005)^(120)} \end{gathered}`

Using a calculator:

A = $2729.095

Rounding to two decimals,

A = $2729.10

Harry will have $2729.10 in his account after 10 years

Now for t = 20 years:

`{\displaystyle A=1500(1+{(0.06)/(12)})^(12\cdot20)}`

Calculating again:

A = $4965.31

Harry will have $4965.31 in his account after 20 years