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 :

Step 1

State the formula for Future value compounded monthly.

[tex]FV=PMT(\frac{(1+i)^n-1)}{i})[/tex]

where;

[tex]\begin{gathered} PMT=878 \\ i=\frac{5.4}{100\times12}=0.0045 \\ n=8\times12=96 \end{gathered}[/tex]

Step 2

Find the future value

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

Find how much of the future value is interest

[tex]\text{Money paid in = 878}\times8\times12=\text{ \$84288}[/tex][tex]\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}[/tex]

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

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