Question

The town of Escalon is issuing 10-year savings bonds so that they can build a new hospital. When the bonds mature the town will owe $3,250,000 to the bondholders. How much will the town need to deposit each quarter into a savings account with an APR of 2.25% in order to have enough to pay the bondholders upon maturity? Round your answer to 2 decimal places

Answer 1

$2,620,122.54

Explanation:

Using the formula for calculating compound interest expressed as;

A = P(1+r/n)^nt

A is the amount = $3,250,000

P is the principal = x

t is the time = 10 years

r is the rate = 2.25% = 0.0225

n = (1/4)year (depositing each quarter)

Substituting the given values into the expression and get P as shown;

$3,250,000 = P(1+0.0225(4))^10(1/4)

$3,250,000 = P(1+0.09)^2.5

$3,250,000 = P(1.09)^2.5

$3,250,000 = P(1.2404)

P = $3,250,000/1.2404

P = $2,620,122.54

Hence the town need to deposit $2,620,122.54 each quarter into a savings account with an APR of 2.25% in order to have enough to pay the bondholders upon maturity