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

Question

4. Finding the interest rate and the number of years AaAa 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 $9,200 will be worth $13,517.82 five 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? O 6.81% ? 8.00% ? 6.40% ? 0.29% If an investment of $45,000 is earning an interest rate of 4.00%, compounded annually, then it will take for this investment to reach a value of $60,389.66-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 An investment of $50 at an annual rate of 5% will return a higher value in five years than $25 invested at an annual rate of 10% in the same time. O An investment of $25 at an annual rate of 10% will return a higher value in five years than $50 invested at an annual rate of 5% in the same time.

Explanation / Answer

1. Answer is 8.00%

Implied Interest Rate = (Future value / Present value)^(1/Years) - 1

Implied Interest Rate = (13517.82 / 9200)^(1/5) - 1

Implied Interest Rate = 8.00%

2. Answer is ~ 7.5 years

Interest Rate = (Future value / Present value)^(1/Years) – 1

4% = (60389.66/45000)^(1/Years) – 1

1.04 = 1.3420^(1/Years)

1.04^Years = 1.3420

Applying natural log at both the sides:

Years x ln(1.04) = ln(1.3420)

Years = 0.294155 / 0.039221

Years = 7.5

3.

Correct option is first option > An investment of $50 at an annual rate of 5% will return a higher value in five years than $25 invested at an annual rate of 10% for same time.

Working as proof:

Case 1: FV = 50 x (1+5%)^5 = $63.81

Case 2: FV = 25 x (1+10%)^5 = $40.26

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