Question

Recently, more money 4u offered a annuity that pays 5.4% compounded monthly. If 878 is deposited into this annuity every month, how much is in the account after 8 years ? How much of this is interest

Answer 1

Step 1

State the formula for Future value compounded monthly.

`FV=PMT(((1+i)^n-1))/(i))`

where;

`\begin{gathered} PMT=878 \\ i=(5.4)/(100*12)=0.0045 \\ n=8*12=96 \end{gathered}`

Step 2

Find the future value

`\begin{gathered} FV=878(\frac{(1+0.0045)^(96)-1^{}}{0.0045}) \\ FV=878(\frac{(1.0045)^{96^{}}-1}{0.0045}) \\ FV=(473.1042497)/(0.0045) \\ FV=105,134.2777 \\ FV\approx\text{ \$105134.28 to 2 decimal places} \end{gathered}`

Find how much of the future value is interest

`\text{Money paid in = 878}*8*12=\text{ \$84288}`
`\begin{gathered} \text{Interest}=\text{ Future value - money paid in=}105134.27771-\text{ 84288}= \\ \text{Interest}=105134.27771-\text{ 84288}=20846.2777 \\ \text{Interest}\approx\text{\$}20846.28\text{ to 2 decimal places} \end{gathered}`

Hence, the answers are;

How much is in the account after 8 years = $105134.28 to 2 decimal places

How much of this is interest = $20846.28 to 2 decimal places