4. Finding the interest rate and the number of years The future value and presen

Question

4. Finding the interest rate and the number of years The future value and present value equations also help in finding the interest rate and the number of years that correspond to present and future value calculations. If a security currently worth $5,600 will be worth $7,054.39 three years in the future, what is the implied interest rate the investor will earn on the security-assuming that no additional deposits or withdrawals are made? 1.26% 0 6.40% 8.00% o 0.42% If an investment of $50,000 is earning an interest rate of 12.00%, compounded annually, then it will take for this investment to reach a value of $116,978.27-assuming that no additional deposits or withdrawals are made during this time. Which of the following statements is true-assuming that no additional deposits or withdrawals are made? O It takes 14.21 years for $500 to double if invested at an annual rate of 5%. 0 lttakes 10.50 years for $500 to double if invested at an annual rate of 5%.

Explanation / Answer

1. PV = 5600
FV = 7054.39
Time = 3years
Rate = (FV/PV)1/3-1 =(7054.39/5600)1/3-1 = 8%

2.PV = 50000
FV = 116,978.27
Rate = 12%
FV = PV*(1+r)n
Applying log on both side
log (116,978.27/50000) = n log(1.12)
n = 7.5 years

3) Applying Rule of 72
if Rate = 5%Then Number of Years 72/5% = 14.4% approx
So option a14.21% is correct

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