Question

A state savings bond can be converted to $100 at maturity six years from purchase. If the state bonds pay 8% annual interest (compounded annually), at what price must the state sell its bonds

Answer 1

The state must sell its bonds at the price of $63.02.

Step-by-step explanation:

The at which the state must sell its bond can be calculated using the present value (PV) as follows:

PV = FV / (1 + r)^n ......................... (1)

Where;

PV = Present value or the price at which the state must sell its bond = ?

FV = Future value of the bond or the value the state savings bond can be converted to at maturity = $100

r = Annual interest rate = 8%, or 0.08

n = number of years = 6

Substituting the values into equation (1), we have:

PV = $100 / (1 + 0.08)^6

PV = $100 / (1.08)^6

PV = $100 / 1.586874322944

PV = $63.02

Therefore, the state must sell its bonds at the price of $63.02.