Question

In: Finance

Suppose you will receive $1,000 in 6 years. If your opportunity cost is 7% annually, what...

  1. 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?

Solutions

Expert Solution

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%

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