Question

(1 point) Irene plans to retire on January 1, 2020. She has been preparing to retire by making annual deposits, starting on January 1, 1980, of $2300 into an account that pays 10% compounded annually. She continued this practice every year through January 1, 2001.

If her goal is to have $1.45 million saved at the time of her retirement, how large should her annual deposits be from January 1, 2002 until January 1, 2020 so that she can reach her goal?

Answer 1

Answer :

Deposits from January 1, 1980 to January 1, 2001 :

Annual deposit (A) = $2,300

Future worth (FW) = ?

Rate of interest (r) = 0.10

Number of years (n) = 21

FV = A * [ ( 1 + r )^n - 1 ] / r * ( 1 + r )

= 2,300 * [ ( 1 + 0.10 )^21 - 1 ] / 0.10 * ( 1 + 0.10 )

= 2,300 * 6.4002 * 1.10 / 0.10

FV = 161,925.06

Therefore, at the end of 2001 she accumulates $ 161,925.06

Now, she requires a total of $ 1,450,000

Difference = $ 1,450,000 - $ 161,925.06 = $ 1,288,074.94

Deposits from January 1, 2002 to January 1, 2020 :

Annual deposit (A) = ?

Future value (FV) = $ 1,288,074.94

Annual interest (r) = 0.10

Number of years (n) = 18

FV = A * [ ( 1 + r )^n - 1 ] / r * ( 1 + r )

1,288,074.94 = A * [ ( 1 + 0.10 )^18 - 1 ] / 0.10 * ( 1 + 0.10 )

1,288,074.94 = A * 4.55992 * 1.10 / 0.10

1,288,074.94 = A * 50.15912

A = 1,288,074.94 / 50.15912

Therefore,

Annual deposit is $ 25,679.78