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 is 4.00%.

Answer 1

Answer:

Present value of payments to the bank=938.51

Explanation:

The present value of the payment to the bank are an ordinary annuity i.e equal payments made at the end of each year for 16 years.

The Present value of an ordinary annuity  is calculated as follows:

$Present value =PMT*\frac{[1-(1+i)^-^n]}{i}$

where PMT is the annual payment made at the end of each year=$100;

i is the interest rate or discount rate = 4%,

n=the number of years the periodic payment of 100 is to be made=12

Present value of payments to the bank = $100*\frac{[1-(1+0.04)^-^1^2]}{0.04}$  = 938.51