Answer:
Explanation:
You need to use the formula to calculate the future value of a constant annual deposit:
[tex]Future\text{ }value=Deposit\times \bigg[\dfrac{(1+r)^n-1}{r}\bigg][/tex]
Where r is the expected percent return, and n the number of years.
1. For a deposit of $30,800 at the end of each year for the next 11 years, with 7% interest.
You will have saved:
[tex]Future\text{ }value=\$ 30,800\times \bigg[\dfrac{(1+0.07)^{11}-1}{0.07}\bigg][/tex]
[tex]Future\text{ }value=\$ 30,800\times 15.7835993=\$486,134.86[/tex]
2. For a deposit of $33,300 each year, for the same number of years and with the same interest rate.
You will have saved:
[tex]Future\text{ }value=\$ 33,300\times \bigg[\dfrac{(1+0.07)^{11}-1}{0.07}\bigg][/tex]
[tex]Future\text{ }value=\$ 33,300\times 15.7835993=\$525,593.86[/tex]
3. For a deposit of $30,800 each year, but with 11 percent interest, for 11 years.
[tex]Future\text{ }value=\$ 30,800\times \bigg[\dfrac{(1+0.11)^{11}-1}{0.11}\bigg][/tex]
[tex]Future\text{ }value=\$ 30,800\times 19.56143=\$602,492.04[/tex]
