Asked by Bailey Hembree on Jun 10, 2024
Verified
A $6300 face-value investment earning interest at 10% compounded annually for a six-year term was sold for $7550. How many years before its maturity date was the note sold if it was discounted to yield 12% compounded monthly?
A) 2.73
B) 3.27
C) 4.50
D) 12.38
E) 39.28
Compounded Annually
A method where interest is added to the principal balance once a year, affecting the total interest earned or paid.
Compounded Monthly
A method of calculating interest where interest earned is added to the principal monthly, so each subsequent interest calculation is on an increased amount.
- Calculate the duration needed for investments to increase, decrease, or reach maturity at certain interest rates.
- Determine the effect of interest rates on the valuation of bonds and securities prior to their maturity.
Verified Answer
AD
Aodhbha DonovanJun 11, 2024
Final Answer :
B
Explanation :
The note was sold 3.27 years before its maturity date. To find this, first calculate the future value of the investment at maturity using the formula for compound interest: FV = PV(1 + r)^n, where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years. Here, FV = $6300(1 + 0.10)^6 = $8953.23. Then, to find when the note was sold, use the formula for present value of a future amount discounted at a different rate compounded differently: PV = FV / (1 + r/m)^(mn), where m is the number of compounding periods per year, r is the annual discount rate, and n is the number of years until maturity. Solving $7550 = $8953.23 / (1 + 0.12/12)^(12n) gives n ≈ 3.27 years.
Learning Objectives
- Calculate the duration needed for investments to increase, decrease, or reach maturity at certain interest rates.
- Determine the effect of interest rates on the valuation of bonds and securities prior to their maturity.