Question

7. Calculate annuity cash flows Your goal is to have $10,000 in your bank account by the end of eight years. If the interest rate remains constant at 10% and you want to annual identical deposits, you'll have to deposit into your account at the end of each year to reach your goal. If your deposits were made at the beginning of each year rather than an at the end, the amount of your deposit would change by still wanted to reach your financial goal by the end of eight years. If you

Answer 1

Your goal is to have $10000 in your bank account by the end of eight years. if the interest rate remains constant at 10% and you want to take annual identical deposits, you will have to deposit $1249.65 into the account at the end of each year to reach your goal.

working note:

let interest be i and the annual deposit be x

year	calculations
1	x
2	x + 1i
3	x + 2 i
4	x + 3 i
5	x + 4i
6	x + 5i
7	x + 6 i
8	x + 7i
total	8x + 28i	$10000

8x + 28i = 10000

8x + 28 x 10% = 10000

8x = 10000 - 2.8

x = 10000 - 2.8 / 8

x = $1249.65

If your deposits were made at the beginning of each year rather that at the end, the amount of your deposit would change by $1249.55 if you still wanted to reach your financial goal by the end of eight years.

working note:

let interest be i and the annual deposit be x

year	calculation
1	x + i
2	x + 2i
3	x +3 i
4	x +4 i
5	x +5 i
6	x + 6i
7	x +7 i
8	x + 8i
total	8x + 36i	$10000

therefore, 8x + 36 i = $10000

8x + 36 x 10% = 10000

8x = 10000 - 3.6

x = 10000 - 3.6 / 8

x = $1249.55