Question

Rachel invests $25,000 at age 25. She hopes the investment will be worth $125,000 when she turns 50. If the interest compounds continuously, approximately what rate of growth will she need to achieve her goal? Round to the nearest tenth of a percent.

Answer 1

The rate of growth will she need to achieve her goal is 2.8%

The formula for finding the compound amount is expressed as:

$A =P(1+\frac{r}{n} )^{nt}$

P is the amount invested = $25000

t is the time in years = 25 years

A is the amount = $125000

r is the rate in %

Substitute the given parameters into the formula to have:

$125000 =25000(1+r )^{25}\\5 =(1+r)^{25}\\log5=25log(1+r)\\log(1+r)=\frac{log5}{25} \\log(1+r)=0.02796\\1+r = e^{0.02795}\\1+r=1.0283\\r = 1.0283 -1\\r = 0.0283$

Hence the rate of growth will she need to achieve her goal is 2.8%

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