A homeowner in a sunny climate has the opportunity to install a solar water heat

Question

A homeowner in a sunny climate has the opportunity to install a solar water heater in his home for a cost of Dollar 2, 600. After installation the solar water heater will produce a small amount of hot water every day, forever, and will require no maintenance. How much must the homeowner save on water heating costs every year if this is to be a sound investment? The interest rate is 5% per year. An annuity pays S50 per year for 22 years. What is the future value (FV) of this annuity at the end of those 22 years, given that the discount rate is 7%? Clarissa wants to fund a growing perpetuity that will pay Dollar 4, 000 per year to a local museum, starting next year. She wants the annual amount paid to the museum to grow by 4% per year. Given that the interest rate is 9%, how much does she need to fund this perpetuity? You plan to deposit Dollar 500 in a bank account now and $300 at the end of the year. If the account earns 3% interest per year, what will be the balance in the account right after you make the second deposit? The balance in the account right after you make the second deposit will be Round to the nearest dollar. Which of the following investments has a higher present value, assuming the same strictly positive interest rate applies to both investments?

Explanation / Answer

1. let they save x amount each year forever

interest rate = 5%

2600 = X/.05

X = 2600*.05 = $130

2)

FV of annuity = 50*FVIFA(7,22)

FVIFA(r,n) = [(`1+r)^n-1]/r

FV= 50*49.0057 = $2450.29

3)

PV of growing perpetuity = 4000/(.09-.04) = $80000

4)

interest rate = 3%

FV right adfer the second installment = 500*1.03+300 = $815

5) investment Y has the higher value because it has higher cash flow in the starting year

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