Question

Mr Wilinks deposited $1,500 in a new account at his bank. The bank pays 4.25% interest compounded semi-annually on this account.Mr Wilinks makes no additional deposits or withdrawals.What is the compound interest earned from the account at the end of 5 years.

Answer 1

The final value of an investment with compounded interest can be found by using the expression below:

`A=P\cdot(1+(r)/(n))^(nt)`

Where A is the final amount, P is the initial amount, r is the interest rate, n is the number of times it is compounded in a year and t is the time elapsed in years.

In this case the interest is compounded semianually, this means that the amount is compounded twice per year. Applying these data on the expression we have:

`\begin{gathered} A=1500\cdot(1+(0.0425)/(2))^(2\cdot5) \\ A=1500\cdot(1+0.02125)^(10) \\ A=1500\cdot(1.02125)^(10)=1851.02 \end{gathered}`

The interest earned is the difference between the final value and the invested one.

`\text{interest}=1851.02-1500=351.02`

The amount earned in interest at the end of the 5 years was $351.02