Question

Time value An Iowa state savings bond can be converted to ​$750 at maturity 5 years from purchase. If the state bonds are to be competitive with U.S. savings​ bonds, which pay 5​% annual interest​ (compounded annually), at what price must the state sell its​ bonds? Assume no cash payments on savings bonds prior to redemption. Ignore taxes.

Answer 1

$78.35

Step-by-step explanation:

Given:

Future value = $750

Maturity time = 5 years

Annual rate = 5%

Now,

Future value = P × ( 1 + r )ⁿ

Where, P is the present value of the bonds

r is the rate of interest

n is number of periods

on substituting the values, we get

$100 = P × ( 1 + 5% )⁵

or

$100 = P × ( 1.05 )⁵

or

P = $78.35

Hence, the state should sell its bond at a price of $78.35