Question

$137 000 is invested for 2 years at 5.5% p.a. compounded monthly. Calculate the interest earned.

Answer 1

The compound interest formula is an equation that lets you estimate how much you will earn with your savings account. It's quite complex because it takes into consideration not only the annual interest rate and the number of years but also the number of times the interest is compounded per year.

The formula for annual compound interest is as follows:

`Fv=P(1+(r)/(m))^(m\cdot t)`

Where:

Fv = future value of the investment

P = initial balance or the value of the investment

r = the annual interest rate (in decimal)

m = the number of times the interest is compounded per year (compounding frequency)

t = the numbers of years the money is invested for

From the problem we have:

`\begin{gathered} P=137,000 \\ t=2 \\ r=0.055 \\ m=12 \end{gathered}`
`\begin{gathered} Fv=137,000(1+(0.0055)/(12))^(12\cdot2) \\ Fv=137,000(1.00458)^(24) \\ Fv=137,000(1.11591)^{} \\ Fv=152,892 \end{gathered}`

With Fv we have the final value to know when we win we have to subtract Fv-P

`Fv-P=152,892-137000=15,892`

$ 15,892 earned from the 2 years invested