Question

What annual rate of return is implied on a $2,500 loan taken next year when $3,625 must be repaid in year 4? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Find Annual rate of return %

Answer 1

We can use the concept of time value of money to solve the question. According to the concept of time value of money, the worth of money today is more than the worth of the same sum of amount at some future time. This is because of the earning potential of money, which means we can earn interest on the money we have now. The equation of time value of money is:
Future value=(Present value)*(1+interest rate)^Time period
Given that the loan must be repaid in year 4.
Now, as the loan is taken next year, the time period will be 4-1=3

Present value=$2,500
Future value=$3,625
We need to calculate the interest rate.
Substituting the given values in the equation, we get;

3625=(2500)*(1+Interest rate)^3
(1+Interest rate)^3=3625/2500
1+Interest rate=(3625/2500)^(1/3)
Interest rate=(3625/2500)^(1/3)-1
=(1.45)^(1/3)-1
=0.13185 or 13.19% (Rounded to two decimal places)
So, the annual rate of return is 13.19%