## Answers

**1]**

future value = present value * (1 + rate of return)^{number of years}

$20,000 = present value * (1 + 4.5%)^{5}

present value = $20,000 / 1.045^{5}

present value = $16,049.02

**2]**

Ending value = starting value * (1 + growth rate)^{number of years}

$73,800 = $52,500 * (1 + growth rate)^{4}

growth rate = ($73,800 / $52,500)^{1/4} - 1

growth rate = 8.89%

**3]**

future value = present value * (1 + rate of return)^{number of years}

$3,500 = $2,500 * (1 + 8%)^{number of years}

(3500 / 2500) = 1.08^{number of years}

number of years = log_{1.08}(3500/2500)

number of years = 4.37 years

**4]**

future value = present value * (1 + rate of return)^{number of years}

$20,000,000 = $12,000,000 * (1 + 10%)^{number of years}

number of years = log_{1.10}(20,000,000 / 12,000,000)

number of years = 5.36 years

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