Suppose a bank decides to make a mortgage loan to an individual so that she may purchase a home. The homeowner will pay the bank $1,500 per month in mortgage payments for the next thirty years. The bank will collect the mortgage payments at the end of the month. What is this promised stream of cash flows worth to the bank today if they could reinvest the monthly income at an annualized rate of 5% for the entire investment horizon?

The answer is $279,422.42

Explanation:

The promised stream of cash flows can be calculated using the below formula

=PMT*((1-(1+(i/t))^(-n*t))/(i/t))

PMT is the periodic mortgage payment of $1,500

i is the interest rate of 5% annualized rate

n is number of years which 30 years

t is the period in a year ,12 months

=1500*((1-(1+(5%/12))^(-30*12))/(5%/12))

=$279,422.42

The promised stream of cash flows worth $279422.42

Ordinarily, n would have been 30 years, but since we are looking the cash flows from a monthly perspective and there 12 months in a year, the best bet is to multiply 30 by 12 (30 years where each year has 12 months)

the investment was $14,174.196

explanation:

a lump sum means that the father of the example made one deposit and leave it be.

we need to know the value of a capital that generated at 4.05% per year during 28 years the sum of $48,613.24

now clearing the formula to solve for capital we got:

and we reach the answer investment = $14,174.20

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