A $400 investment has doubled to $800 in six years because of a 12.25% return. How much longer will it take for the investment to reach $1100 if it continues to earn 12.25%?
A) 2.56 years
B) 2.76 years
C) 3.46 years
D) 5 years

Question

Quizplus · Accepted Answer

To solve this problem, we can use the formula for compound interest:

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

where A is the final amount, P is the principal (initial investment), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

Using the given information, we know that P = 400, A = 1100, r = 0.1225, and n = 1 (compounded yearly). We can solve for t by substituting these values into the formula and solving for t:

1100 = 400(1 + 0.1225/1)^(1t)
2.75 = (1.1225)^t
log(2.75) = t*log(1.1225)
t = log(2.75)/log(1.1225)
t ≈ 2.76 years

Therefore, it will take approximately 2.76 more years for the investment to reach $1100 if it continues to earn 12.25% per year.

A $400 Investment Has Doubled to $800 in Six Years