Question

Tremont is estimating the expenses he may incur for roof repairs to his house. He is expecting that he will have to replace the roof 20 years from now. It currently costs $25,000 to replace a roof on a house like his. If he expects 3% annual inflation, how much does he have to invest at the beginning of each year at a 6% annual interest rate to have enough to cover the expected roof replacement 20 years from now?

Answer 1

Cost of replacing roof in 20 years = current cost * (1 + inflation rate)20

Cost of replacing roof in 20 years = $25,000 * (1 + 3%)20 = $45,152.78

Next, we calculate the yearly saving required to accumulate the required amount in 20 years. The yearly saving required is calculated using PMT function in Excel :

rate = 6% (rate of return earned)

nper = 20 (number of years until retirement)

pv = 0 (amount currently saved is zero)

fv = 45152.78 (required amount at retirement)

type = 1 (each saving is at the beginning of the year, hence it is an annuity due)

PMT is calculated to be $1,157.98

Annual savings required = $1,157.98