Find the time required for an investment of 5000 dollars to grow to 8800 dollars at an interest rate of 7.5 percent per year, compounded quarterly.

Question

Find the time required for an investment of 5000 dollars to grow to 8800 dollars at an interest rate of 7.5 percent per year, compounded quarterly.

got 7.6 which was wrong, put 8 also wrong, someone help please

Answer 1

Let

p = 0.075 be yearly interest,

A = $5000 be the initial investment,

B = $8800 be the result of compounding,

n (to be found) be the number of quarters of compounding.

Quarterly interest is p/4.

According to the general compounding formula, after n quarters

B = A(1 + p/4)ⁿ

Here are the steps of simplification of the above to obtain n

(1 + p/4)ⁿ = B/A

n log(1 + p/4) = log(B/A)

n = log(B/A)/log(1 + p/4)

Substituting actual numbers

n = log(8800/5000)/log(1 + 0.075/4) = 25.3

So you have to wait 26 quarters, i.e., 6 and a half years.