Question

3. Stan invests $5,000 at age 18. He hopes
the investments will be worth $10,000 when
he turns 25. If the interest compounds
continuously, approximately what rate of
growth will he need to achieve his goal?

Answer 1

Continuous compund interest formula:

A=Pe^(rt)

Where:

A = future vale = $10,000

P = Principal invest = $5,000

r = interest rate

t = time = (25 - 18 ) = 7 years

Replacing:

10,000 = 5,000 e^(7r)

Solve for r:

10,000/5,000 = e^(7r)

2 = e^(7r)

Ln 2 = Ln e^(7r)

Ln 2 = 7r Lne

Ln 2 = 7r

Ln2/7 = r

r= 0.099 (decimal form)

r x 100 = 0.099 x 100 = 9.9 %