Question

Suppose that it is the morning following your 18th birthday. Also assume that every year starting with your 1st birthday, your grandfather deposited a fixed (constant) amount into an account that has paid 8% interest annually. The balance in the account is $200,000. What is the constant payment that your grandfather deposited on each birthday?

Answer 1

The annual deposited amount will be so much that future value of which become equal to current balance.

Amount deposited each birthday

=

Total future value of annuity/Future Value of annuity of 1

=

$ 2,00,000.00

/

37.45024

=

$       5,340.42

Thus,

Amount deposited on each birthday is

$       5,340.42

Working;

Future Value of annuity of 1

=

(((1+i)^n)-1)/i

Where,

=

(((1+0.08)^18)-1)/0.08

i

8%

=

37.45024374

n

18