U4.L4.HW: Exponential & Logarithmic Equations: Question 20

Question

Find the time required for an investment of 5000 dollars to grow to 8500 dollars at an interest rate of 7.5 percent per year, compounded quarterly.

Your answer is t = _____ years.

Answer 1

A = P(1 + r/n)^nt Where A is amount in the account after t periods, P is the initial investment, r is the annual rate (APY) expressed as a decimal, and n is the number of compounding periods/yr.

8500 = 5000(1 + 0.075/4)^4•t -> 0.075/4 = 0.01875 and divide both sides by 5000.

1.7 = 1.01875^4t take log (ln) of both sides

ln(1.7) = 4t(ln 1.01875)

0.53063 = 4t(0.01858)

4t = 0.53063/0.01858 = 28.5592

t = 28.5592/4 = 7.14 years

Check with an online compound interest calculator.