A couple thinking about retirement decide to put aside $2,200 each year in a sav

Question

A couple thinking about retirement decide to put aside $2,200 each year in a savings plan that earns 8% interest. In 5 years they will receive a gift of $28,000 that also can be invested.

(can you please explain the steps)

How much money will they have accumulated 30 years from now? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

If their goal is to retire with $720,000 of savings, how much extra do they need to save every year? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

A couple thinking about retirement decide to put aside $2,200 each year in a savings plan that earns 8% interest. In 5 years they will receive a gift of $28,000 that also can be invested.

(can you please explain the steps)

Explanation / Answer

Solution:

Future Value of Annuity = Annuity * Future Value Annuity Factor (year,roi).

Future Value = Present Value * (1+rate of interest)no of periods

a.) The future value of $2,200 can be calculated using the formula for future value of annuity as it is a continuous series of annuity paid. While, $28,000 is a one-time investment after 5years which can be calculated using future value formula.

Future Value of Annuity

= ($2,200) * 113.2832

= $249,223.04.

Future Value

= ($28,000) * (1+8%)25

= $191,757.305494141

Accumulated Savings = Future Value of Annuity * Future Value = $249,223.04 + $191,757.305494141

Accumulated Savings = $440,980.35.

b.) Additional accumulated savings required = $720,000 - $440,980.345494141 = $279,019.654505859.

Using Future Value of Annuity Formula,

$279,019.654505859 = Annuity * 113.2832

Annuity = $2,463.03

Additional Savings = $2,463.03.

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