Asked by Tanesha Williams on Jun 17, 2024
Verified
A $10,000 debt is repaid by payments of $800 at the end of each quarter for five years. What quarterly-annually compounded nominal interest rate was charged on the loan?
A) 23.10%
B) 4.96%
C) 11.08%
D) 9.81%
E) 19.86%
Nominal Interest
The stated interest rate on a loan or investment, not accounting for inflation or compounding effects.
- Evaluate the critical interest rate to meet a targeted monetary ambition within an established duration.
- Use fiscal formulas to resolve complicated challenges linked to loans, savings, and investment options.
Verified Answer
LS
Lediya SolomonJun 20, 2024
Final Answer :
B
Explanation :
The correct answer is found by using the formula for the present value of an annuity: PV=PMT×[1−(1+r)−nr]PV = PMT \times \left[\frac{1 - (1 + r)^{-n}}{r}\right]PV=PMT×[r1−(1+r)−n] , where PV is the present value (or initial loan amount), PMT is the payment amount per period, r is the interest rate per period, and n is the total number of payments. Rearranging to solve for r when PV = $10,000, PMT = $800, and n = 20 (5 years of quarterly payments), we find that the interest rate that fits these conditions is approximately 4.96% per quarter, compounded quarterly.
Learning Objectives
- Evaluate the critical interest rate to meet a targeted monetary ambition within an established duration.
- Use fiscal formulas to resolve complicated challenges linked to loans, savings, and investment options.
Related questions
What Would Be the Effective Rate of Interest If $100,000 ...
What Compounded Rate of Return Will Allow Investments of $800 ...
A $12,000 Loan Is Repaid by Semi-Annual Payments of $1,500 ...
What Monthly Compounded Nominal Rate of Return Must Rachel Earn ...
If Money Can Earn 6% Compounded Monthly, How Much More ...