Question

1. If you invested $10,000 in an investment account and you expect it to double in 4 years, what interest rate must it earn?
2. What is the future value of a 5-year ordinary annuity of $1000 if the appropriate interest rate is 5%? What is the present value of the annuity?
3. What is the future value of $1000 after 4 years under 10% annual compounding? Semiannual compounding? Quarterly compounding? Monthly compounding? Daily compounding
4. What is the effective annual rate (EAR or EFF%)? What is the EFF% for a nominal rate of 5%, compounded semiannually? Compounded quarterly? Compounded monthly? Compounded daily?
5. Construct an amortization schedule for a $1,000, 12% annual rate loan with 4 equal installments. What is the annual interest expense for the borrower, and the annual interest income for the lender, during Year 2?
6. Suppose on January 1 you deposit $1000 in an account that pays a nominal, or quoted, interest rate of 12%, with interest added (compounded) daily. How much will you have in your account on October 1, or 9 months later?
7. You want to buy a car, and a local bank will lend you $10,000. The loan would be fully amortized over 6 years (72 months), and the nominal interest rate would be 10%, with interest paid monthly. What is the monthly loan payment?
8. While Mary Corens was a student at the University of Tennessee, she borrowed $20,000 in student loans at an annual interest rate of 5%. If Mary repays $200 per year, then how long (to the nearest year) will it take her to repay the loan?

Answer 1

1. PV =10000
FV =20000
Number of years =4
Rate =(FV/PV)^(1/n)-1 =(2)^(1/4)-1 =18.92%

2. Number of years =5
PMT =1000
Rate =5%
FV of annuity =PMT*((1+r)^n-1)/r) =1000*((1+5%)^5-1)/5%) =5525.63
PV of annuity =PMT*((1-(1+r)^-n)/r =1000*((1-(1+5%)^-5)/5%) =4329.48

3. Rate =10%
Number of years =4
PV =1000
FV at annual compounding=PV*(1+r)^n =1000*(1+10%)^4 =1464.10
FV at semi annual compounding =PV*(1+r/2)^2n =1000*(1+10%/2)^8 =1477.46
FV at quarterly compounding =PV*(1+r/4)^4n =1000*(1+10%/4)^16 =1484.51
FV at semi annual compounding =PV*(1+r/2)^2n =1000*(1+10%/12)^48=1489.35

4. Nominal Rate =5%
EAR is the interest which includes the number of compounding and also EAR is always greater than APR if number of compounding is greater than 1.
EAR at Semi annual rate =(1+APR/2)^2-1 =(1+5%/2)^2-1 = 5.06%
EAR at quarterly rate =(1+APR/4)^4-1 =(1+5%/4)^4-1 = 5.09%
EAR at monthly rate =(1+APR/12)^12-1 =(1+5%12)^12-1 =5.12%
EAR at daily rate =(1+APR/365)^365-1 =(1+5%/365)^365-1 = 5.13%