Question

How long will it take for a $4000 investment to grow to $5000 at an annual rate of 12%, compounded semiannually? Assume that no withdrawals are made. Do not round any intermediate computations, and round your answer to the nearest hundredth.

Answer 1

Answer: We have the following formula to solve this problem. Using compound interest formula i.e.

where "A" is the ending amount, "P" is the beginning amount (or "principal"), "r" is the interest rate (expressed as a decimal), "n" is the number of compoundings a year, and "t" is the total number of years.

Now, given in question we have

P = $ 4000

A = $ 5000

r = 12\100 = 0.12

n = 2 (semiannual, compounding twice in a year)

Putting all the values in the above-given formula to find t (time)

t = 1.915 years

So the required time

t = 1.915 years

Thank you!!