5) What is the effective annual interest rate for a loan with a nominal annual i
ID: 2816078 • Letter: 5
Question
5) What is the effective annual interest rate for a loan with a nominal annual interest rate of 12% if compounded:
semi-annually. Answer ____________________
monthly. Answer _________________________
continuously. Answer _____________________
6) You make a series of quarterly deposits every quarter starting at the end Quarter 1 and ending at the end of Quarter 36. The first deposit is $1,100, and each deposit increases by $500 each Quarter. The nominal annual interest rate is 7%, and is compounded continuously. What is the Future Value of these series of deposits at the end of Quarter 36?
Answer _____________________
Explanation / Answer
Answer to Question 5:
Answer a.
Annual Interest Rate = 12%
Semiannual Interest Rate = 6%
Effective Annual Rate = (1 + Semiannual Interest Rate)^2 - 1
Effective Annual Rate = (1 + 0.06)^2 - 1
Effective Annual Rate = 1.1236 - 1
Effective Annual Rate = 0.1236 or 12.36%
Answer b.
Annual Interest Rate = 12%
Monthly Interest Rate = 1%
Effective Annual Rate = (1 + Monthly Interest Rate)^12 - 1
Effective Annual Rate = (1 + 0.01)^12 - 1
Effective Annual Rate = 1.1268 - 1
Effective Annual Rate = 0.1268 or 12.68%
Answer c.
Continuous Interest Rate = 12%
Effective Annual Rate = exp(0.12) - 1
Effective Annual Rate = 1.1275 - 1
Effective Annual Rate = 0.1275 or 12.75%
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