Question

Find the time required for an investment of $5000 to grow to $8000 at an interest rate of 7% per year if it is compounded quarterly

Answer 1

Answer:

7 years

Step-by-step explanation:

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

where A is the final amount, P is the initial amount, r is the interest rate, and n is the number of times of compounding.

Compounded quarterly means compounded 4 times per year.  So the effective interest rate per compounding is:

r = 0.07 / 4

r = 0.0175

Given that A = 8000 and P = 5000:

8000 = 5000 (1 + 0.0175)^n

1.6 = 1.0175^n

log 1.6 = n log 1.0175

n = (log 1.6) / (log 1.0175)

n ≈ 27.1

Rounding up to the nearest whole number, it takes 28 compoundings.  Since there's 4 compoundings per year:

t = 28 / 4

t = 7

It takes 7 years.