Question

Assume your goal in life is to retire with three million dollars. How much would you need to save at the end of each year if interest rates average 5% and you have a 10-year work life (the closest answer)

Answer 1

$200,000 every year

Step-by-step explanation:

Assuming you are saving without compounding your interest

Applying the Simple interest/Formula

A = P (1 + rt)

A = final amount

P = initial principal balance

r = annual interest rate

t = time (in years)

Given A=$3,000,000

P=?

r=5%

t=10 years

Substituting we have

Calculation:

First, converting R percent to r a decimal

r = R/100 = 5%/100 = 0.05 per year.

Solving our equation:

3,000,000 = P(1 + (0.05 × 10)

3,000,000 = P(1 + (0.5)

3,000,000 = 1.5P

P=3,000,000/1.5

P=$2,000,000

The amount to be saved at 5% interest rate per year is

2,000,000/10

$200,000 every year

Answer 2

Annual savings = $238,512

Step-by-step explanation:

Given Data:

Interest rate (r) = 5%

Number of years (n) = 10 years

Future value (Fv) = $3,000,000

Annual savings = ?

Calculating the future value of annuity factor using the formula;

Future value annuity factor (r%, n) = [(1 + r)¹⁰ - 1]/r

Substituting, we have

Future value annuity factor (5%, 10) = [(1 + 0.05)¹⁰ - 1]/0.05

= [(1.05)¹⁰ - 1]/0.05

= (1.6289 - 1)/0.05

= 0.6289/0.05

= 12.578

But,

Future value = Annual savings x Future value annuity factor (r%, n)

Substituting, we have

$3,000,000 = Annual savings x 12.578

Annual savings = 3,000,000/12.578

= $238,512