Question

You have $50,000 in savings for retirement in an investment earning a stated annual rate of 5%, compounded semi-annually. You aspire to have $1,000,000 in savings when you retire. Assuming you add no more to your savings, how many years will it take to reach your goal?

A. 20 years

B. 25 years

C. 30 years

D. 35 years

Answer 1

To calculate the number of years it will take to reach your retirement savings goal of $1,000,000 with compound interest, use the formula A = P(1 + r/n)^(nt). Plugging in the given values, the calculation yields approximately 29.5 years. Hence, C) is correct.

Step-by-step explanation:

To calculate the number of years it will take to reach your retirement savings goal of $1,000,000, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment

P = the principal (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

Plugging in the given values:

$1,000,000 = $50,000(1 + 0.05/2)^(2t)

Divide both sides by $50,000:

20 = (1 + 0.05/2)^(2t)

Take the logarithm of both sides:

ln(20) = 2t * ln(1 + 0.05/2)

t ≈ ln(20) / (2 * ln(1 + 0.05/2))

Using a calculator, we find that t ≈ 29.5

Therefore, it will take approximately 29.5 years to reach your retirement savings goal of $1,000,000.