Question

Sofia has a government bond that will be worth $500 when it matures in 5 years. She wants to sell it to her brother because she needs the cash now for car repairs. Assuming an interest rate of 3% and assuming monthly compounding, what is the present value of the bond?

Answer 1

$413.20

Explanation:

To find the present value of the bond, we need to calculate the amount of money Sofia would need to have today in order to receive $500 in 5 years, considering an interest rate of 3% with monthly compounding.

The formula we can use to calculate the present value is:

Present Value = Future Value / (1 + interest rate)^n

Where: - Future Value is the amount the bond will be worth at maturity ($500) - Interest rate is the annual interest rate (3% or 0.03) - n is the number of compounding periods (5 years * 12 months = 60 months)

Plugging in the values into the formula, we have:

Present Value = $500 / (1 + 0.03/12)^60

Calculating this expression, we get:

Present Value ≈ $413.20 (rounded to the nearest cent)