Question

How much money should Timothy and Tiffany deposit annually for 20 years in order to provide an income of $30,000 per year for the next 10 years? Assume an interest rate is a constant 4%

Answer 1

Answer: $8,171.44

Explanation:

The present value of the income of 10 years now is the future value of the payments in 20 years.

The present value is therefore;

= 30,000 * Present value of annuity interest factor, 4%, 10 years

= 30,000 * 8.111

= $243,330‬

As  $243,330‬ is the future value of the payments in 20 years.

The payment is therefore;

243,330‬ = Payment * Future value of annuity interest factor, 4%, 20 years

243,330 = Payment * 29.7781

Payment = 243,330/29.7781

= $8,171.44

Answer 2

Answer:

$8,171.37

Explanation:

first we must find the value of their account before they start receiving the distributions, (i.e. how much money they need to have in 20 years):

present value = annual payments x annuity factor

• annual payments = $30,000
• annuity factor (PV, 4%, 10 periods) = 8.1109

present value = $30,000 x 8.1109 = $234,327

now we need to calcualte the annual contribution in order to have $234,327 in 20 years:

future value = annual payment x annuity factor

annual payment = future value / annuity factor

• future value = $234,327
• annuity factor (FV, 4%, 20 periods) = 29.778

annual payment = $234,327 / 29.778 = $8,171.37