In: Finance
Suppose you will receive $1,000 in 6 years. If your opportunity
cost is 7% annually, what is the present value of this amount if
interest is compounded every six months?
What is the effective annual rate?
Present value of money: | = | FV/ (1+r/M) ^MN | |
Future value | FV= | 1,000.00 | |
Rate of interest | r= | 7.0% | |
Number of compounding periods in a year | M= | 2 | |
Number of years | N= | 6 | |
Present value | = | 1000/ (1+0.07/2)^6 × 2 | |
= | $ 661.78 |
Present value is $661.78
EAR:
Effective annual interest rate= | (1+periodic interest rate)^m -1 | |
rs= | Stated interest rate | 7.00% |
m | number of compoundings in a year | 2 |
rs/m | period interest rate | 3.5000000% |
Effective annual interest rate= | (1+0.035)^2 -1 | |
Effective annual interest rate= | 7.12% |