Question

1.If you invest $5,867 today and in years 1, 2 and 3 in an account that earns 4.71% APR (compounded annually), how much will you have in the account in 16 years?

2.You plan on purchasing a new car in 11 months. The cost of the car in 11 months will be $25,813. How much would you have to invest today to exactly pay for the new car if you investments earn 3.74% APR (compounded monthly)?

3.

You want to save an amount today that will pay for your future annual food bills that will start next year, and go for 29 years.

The current annual cost of your food bill is $8,110, but the cost is rising at 3% per year.

How much would you have to invest today, to fully pay for your future annual food bills if your investments earn 6.30% APR nominal (annual compounding).

Answer 1

1.

The deposited amount today will grow for 16 years, the amount of year1 will grow for 15 years, year 2 will grow for 14 years and year 3 will grow for 13 years

So the amount at year 16 = 5867(1.0471^16) + 5867(1.0471^15) + 5867(1.0471^14) + 5867(1.0471^13) = 45,801.446

2.

The future value or the price of the car after 11 months = 25,813

Return on monthly basis = 3.74%/12 = 0.317%

(Amount Invested today)*(1.00317^11) = 25,813

Amount Invested today = $24,929.79

3.

Todays bill = 8110

Growth rate of bill = 3%

Investment return = 6.30%

Amount Invested today = PV of all the future bills = (8110*1.03)/1.063 + (8110*1.03^2)/(1.063^2) + (8110*1.03^3)/(1.063^3) + (8110*1.03^4)/(1.063^4) + ------------ + (8110*1.03^29)/(1.063^29)

Using sum of GP formula,

Amount Invested today = 8110(1.03/1.063)(1 - (1.03/1.063)^29)/(1 - (1.03/1.063)) = $151,702.0409