A local bank advertises the following deal: Pay us $100 at the end of each year

Question

A local bank advertises the following deal: Pay us $100 at the end of each year for 12 years and then we will pay you (or your beneficiaries) $100 at the end of each year forever. a. Calculate the present value of your payments to the bank if the interest rate available on other deposits is 5.00%. (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What is the present value of a $100 perpetuity deferred for 12 years if the interest rate available on other deposits is 5.00%. (Do not round intermediate calculations. Round your answer to 2 decimal places.) c. Is this a good deal? No Yes

Explanation / Answer

PV of a cash flow = CFi/(1+d)i

CF = 100

N = 12 year i.e. i = 1 to 12

d = 5%

a. PV = 886.33

FV of perpetuity after 12 years = D/r where d is the cash flow till perpetutiy and r is the deposit rate at 5%

FV of perpetuity after 12 years = 100/0.05 = 2000

b. The present value of this perpetutity = 2000/(1+0.05)^12 = 1113.68

c. Since the present value of perpetuity due in 12 years is higher than the present value of cash flows of 100$ for 12 years to the bank, the offer is certainly a good deal. so it is a Yes

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