A real estate investor feels that the cash flow from a property will enable him to pay a lender N$15,000 per year, at the end of every year, for 10 years. How much should the lender be willing to loan him if he requires a 9% annual interest rate (annually discounting, assuming the first of the 10 equal payments arrives one year from the date the loan is disbursed)?
Question
A real estate investor feels that the cash flow from a property will enable him to pay a lender N$15,000 per year, at the end of every year, for 10 years. How much should the lender be willing to loan him if he requires a 9% annual interest rate (annually discounting, assuming the first of the 10 equal payments arrives one year from the date the loan is disbursed)?
Solution
This is a problem of calculating the present value of an annuity. The formula for the present value of an annuity is:
PV = PMT * [(1 - (1 + r)^-n) / r]
where:
- PV is the present value
- PMT is the annual payment
- r is the interest rate
- n is the number of periods
In this case:
- PMT = N$15,000
- r = 9% or 0.09
- n = 10 years
Substituting these values into the formula, we get:
PV = 15,000 * [(1 - (1 + 0.09)^-10) / 0.09]
Solving this equation will give us the amount the lender should be willing to loan the real estate investor.
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