Question

13. Lennox guarantees that its new hot water heater will save any household that has two or more people at least $30 each month in electricity costs beginning 1 month after the hot water heater is installed. If the hot water heater is under warranty for 5 years, the minimum amount a family could afford the heater now would be ________________. Assume that the interest rate is 6 % compounded monthly.

Answer 1

We can use the formula for present value of annuity to determine the minimum amount a family could afford the heater now.

Cost Savings = $30

Time = 5 * 12 = 60 periods ( monthly compounding )

Rate = 6% = 6 / 12 = 0.50% ( monthly compounding )

Present Value of Annuity = P * [ 1 - ( 1 + r ) ^-n / r ]

Or,

Present Value of Annuity = 30 * [ 1 - ( 1 + 0.005 ) ^-60 / 0.005 ]

Or,

Present Value of Annuity = 30 * 51.726

Or,

Present Value of Annuity = $1551.77

Therefore,

If the hot water heater is under warranty for 5 years, the minimum amount a family could afford the heater now would be $1551.77.