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 _____________________

Answer 1

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%