Question

You want to be a millionaire when you retire in 35 years. a. How much do you have to save each month if you can earn an annual return of 10.7 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. How much do you have to save each month if you wait 10 years before you begin your deposits? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c. How much do you have to save each month if you wait 20 years before you begin your deposits? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) a. Savings per month starting today b. Savings per month starting in 10 years c. Savings per month starting in 20 years

Answer 1

Time to retire in years = 35

Investment made every month of equal amount.

interest rate = 10.70% p.a; compounded monthly; rate = 10.70% / 12 = 0.89% monthly

Future value = $1,000,000

a) Time period = 35 years; i.e = 35 * 12 = 420 compounding periods

Monthly amount = A

1st month amount A will be invested for 420 months. Second month investment amount is compounded monthly for 419 months and so on.

$1,000,000 = [A(1+0.0089)^420] + [A(1+0.0089)^419] + ....+ [A(1+0.0089)^1]

Solving for A, A = $219.55

b) Time period to invest = 25 years (i.e; 25 * 12 = 300 compounding periods)

$1,000,000 = [B(1+0.0089)^300] + [B(1+0.0089)^299] + ....+ [B(1+0.0089)^1]

Solving for B, B = $668.35

c) Time period to invest = 15 years (i.e; 15 * 12 = 180 compounding periods)

$1,000,000 = [C(1+0.0089)^180] + [C(1+0.0089)^179] + ....+ [C(1+0.0089)^1]

Solving for C, C = $2,261.63

As time for investment is decreased, amount per month to invest has increased.