The future value and present value equations also help in finding the interest r

Question

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 of $14,000 will be worth $23,994 seven years in the future, assuming that no additional deposits or withdrawals are made, what is the implied interest rate the investor will earn on the security?

A. 6.00%

B. 6.40%

C. 8.00%

D. 9.60%

If an investment of $40,000 is earning an interest rate of 8.00% compounded annually, it will take (0.4%, 1.3%, 3.0%, OR 7.9%)   for this investment to grow to a value of $50,388.48—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?

A. It takes 14.2 years for $500 to double if invested at an annual rate of 5%.

B. It takes 10.5 years for $500 to double if invested at an annual rate of 5%.

Explanation / Answer

Answer a.

Present Value = $14,000
Future Value = $23,994
Period = 7 years

Interest Rate = (Future Value / Present Value)^(1/Period) - 1
Interest Rate = ($23,994 / $14,000)^(1/7) - 1
Interest Rate = 1.71386^(1/7) - 1
Interest Rate = 1.08 - 1
Interest Rate = 0.08 or 8.00%

Answer b.

Present Value = $40,000
Future Value = $50,388.48
Annual Interest Rate = 8.00%

Present Value * (1 + Interest Rate)^Period = Future Value
$40,000 * 1.08^n = $50,388.48
1.08^n = 1.259712
n = ln(1.259712) / ln(1.08)
n = 3.0

So, it will take 3 years for this investment to grow to $50,388.48

Answer c.

Amount invested = $500
Desired sum = $1,000
Annual Interest Rate = 5%

Present Value * (1 + Interest Rate)^Period = Future Value
$500 * 1.05^n = $1,000
1.05^n = 2
n = ln(2) / ln(1.05)
n = 14.2

So, it takes 14.2 years for $500 to double if invested at an annual rate of 5%

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