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1) A friend offers you a loan at an interest rate of 0.1% PER DAY. What is the n

ID: 1135235 • Letter: 1

Question

1) A friend offers you a loan at an interest rate of 0.1% PER DAY.

What is the nominal (also known as the APR or Annual Percentage Rate) rate for this loan?

Answer_____________________

What is the effective annual interest rate for his loan?

Answer_____________________

2) You receive payments at the end of each Quarter starting at the end of Quarter 1 and lasting 6 years (so the last payment you receive is at the end of Quarter 24). These payments are an equal series of payments of $1,500 for all 24 payment periods. The interest rate is 9% annual rate compounded monthly. What present value P is equal to this series of 24 payments?

Answer ____________________

3) You make monthly deposits of $1,000 in a bank starting at the end of month 1 and lasting 4 years (the last deposit is at the end of month 48). What is the future value of these deposits right after your last deposit? Assume the nominal annual interest rate is 12% compounded monthly.

Answer: ___________________

4) You make monthly payments on a loan. What is the effective monthly interest rate for a loan with an 8% nominal annual interest rate if the loan is compounded

monthly.         Answer _____________

daily.               Answer ____________

continuously. Answer ___________

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

1)

Effective annual rate = 0.1%*365 (assuming a non leap year) = 36.5% per year

APR is given by 36.5% = (1 + R%/365)^365 - 1

1.365^(1/365) = (1 + R%/365)

This give APR = 31.13%

2)

Quarterly interest rate = 9% x (3/12) = 2.25%

Number of quarters = 24

Present value of series = $1,500 x PVIFA(2.25%, 24)

= $1,500 x 18.3890 [from PVIFA table]

=27,583.5

3)

use calculator

PMT=1000 each month deposit

N=48month

1/Y=12/12=1

PV=0


Future value = $1,000 x Future Value Interest Factor of Annuity (1%, 48 Periods)

       =$1,000 x 61.2226
      
       =$61222.6