Question

2. The city of Glendale borrows $48 million by issuing municipal bonds to help build the Arizona Cardinals football stadium. It plans to set up a sinking fund that will repay the loan at the end of 10 years. Assume a 4 percent interest rate per year. What should the city place into the fund at the end of each year to have $48 million in the account to pay back their bondholders?

Answer 1

Answer:

$5,917, 965.66 per year

Explanation:

The $48 million will represent the value of all annuities after ten years. The get the amount the city of Glendale should be saving each year, we apply the present value of annuity formula, which is as below.

P   = PV ×  r / 1 − (1+r)−n

P is value of each payment

PV = present value of annuity : $48,000,000.00

r =interest rate : 4 % = 0.04

n: number of periods: 10

P = $48,000,000 x {0.04/(1-(1+0.04)-10}

P = $48,000,000 x {0.04/ 1-0.6755641688)

P =$48,000,000x (0.04/0.3244358312)

P= $48,000,000 x 0.123290951

P= 5,917, 965.66 per year