Question

# You are saving for retirement and you want to have \$1,000,000 in 40 years. Suppose you...

You are saving for retirement and you want to have \$1,000,000 in 40 years. Suppose you earn an average return of 5% on all of your investments. How much do you need to set aside each year to reach your goal?

You want to blow all of your retirement savings from the previous problem in 20 years from retirement. You now earn only 2% on your investment returns. How much can you spend each year?

(a) Let the amount set aside each year be P

Number of years = n = 40 years

Future value after 40 years = 1000000

rate of returns = r = 5%

Hence, FV = P(1+r)n-1 +....+ P(1+r)2 + P(1+r) + P = P[(1+r)n -1]/r

=> 1000000 = P(1.0540 -1)/0.05

=> P = \$8278.16

(b) All the investment is used up in 20 years

n = 20 years

rate of return = r = 2%

PV = 1000000

Let amount spent each year be P

=> PV = P/(1+r) + P/(1+r)2 +....+ P/(1+r)n = P[1- (1+r)-n]/r

=> 1000000 = P(1 - 1.02-20)/0.02

=> P = \$61156.72

#### Earn Coins

Coins can be redeemed for fabulous gifts.

##### Need Online Homework Help?

Most questions answered within 1 hours.

##### Active Questions
• A 25 mm diameter egg roll (k = 1 W/m degree Celsius) is roasted with the...
asked 32 seconds ago
• Instruments in airplane A indicate that, with respect to the air, the plane is headed 30°...
asked 9 minutes ago
• You wish to test the following claim (H1H1) at a significance level of α=0.05α=0.05.       Ho:μ=73.9Ho:μ=73.9       H1:μ≠73.9H1:μ≠73.9...
asked 9 minutes ago
• Let X1 and X2 be independent Poisson random variables with respective parameters λ1 and λ2. Find...
asked 14 minutes ago
• You wish to test the following claim (H1H1) at a significance level of α=0.001α=0.001.       Ho:μ=88.8Ho:μ=88.8       H1:μ>88.8H1:μ>88.8...
asked 20 minutes ago
• You have been asked to install floor tiles and paint your aunt’s bathroom based on the...
asked 23 minutes ago
• A new disinfection system is being designed for a treatment plant with a flow of 400...
asked 23 minutes ago
• A produce distributor uses 786 packing crates a month, which it purchases at a cost of...
asked 31 minutes ago
• What do researchers believe explains why some individual to engage in precocious, promiscuous, unprotected sex or...
asked 31 minutes ago
• 4. For a 99% confidence level, how large of a sample size is needed for a...
asked 31 minutes ago
• Another student was upset for a different reason. He thought that Test 2 was too long...
asked 32 minutes ago
• Suppose a marketing company wants to determine the current proportion of customers who click on ads...
asked 37 minutes ago