Question

A homeowner in a sunny climate has the opportunity to install a solar water heater in his home for a cost of $2900. After installation the solar water heater will produce a small amount of hot water every day, forever, and will require no maintenance. The homeowner's water bill is thus lowered by a fixed amount every year, forever. 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.) $145 $160 $175 $190 QUESTION S What is the present value (PV) of an investment that will pay $500 in one year's time, and S500 every year after that in perpetuity when the interest rate is 10%? o$2500 $A000 $3000 $8000 QUESTION An annuity pays $12 per year for 98 years, starting in one year from today. What is the present value (PV) of this annuity given that the discount rate is 7%? $85.60 $171.20 142.67 $199.74

Answer 1

1)The formuale for present value of perpetuity is
investment= fixed cash saving per year/interest rate
given investment=2900
interest rate=5%
savings=2900*5%=145
it is option A

2)present value of perpetuity=amount per year/interest rate
=500/10%
=5000
option D

3)here we use present valyue of annuity formuale
Present value= periodic amount*(1-((1+r)^-n))/r
periodic amount=12
n=98
r=7%
answer is 171.20
option B