Question

Sam borrowed $1000 from Tom and him back with a $2000 check whe he won the powerball after 4 years.

a. What simple interest rate did he pay?

b. If the interest rate is compounded monthly, what is the effective annual interrest rate he paid?

Answer 1

A = P*(1+rt)
where A is the final investment value
P is the principal amount invested
r is the interest rate
2000 = 1000*(1+r4)
2 = 1+4r
4r = 1
r= .25 or 25%
a) The simple interest rate is equal to 25%
Effective annual interest rate = ((1+(i/n))^n)-1
where I is the stated annual interest rate that is 25%
n is the number of compounding periods that is 12
Effective annual interest rate (EAR) = ((1+(.25/12))^12)-1
EAR = .2807
b) The EAR is 28.07%