jimmy invest 18000 in an account that pays 8.24% compounded quarterly. How long(in years and months) will it take for his investment to reach 22000

Question

they want years and months pre cal problem

Answer 1

Hi Maya,

 

The formula for compound interest is

A(t) = A₀ (1+ r/n)^nt

 

A(t) is the amount at time t

A₀ is the initial investment

r is the interest rate, as a decimal

n is the number of times compounded per year

t is the number of years

 

In your problem, you're given

A₀ = 18,000

r = 8.24% = 0.0824

n = 4 (quarterly)

A(t) = 22,000

and you need to solve for t

 

22,000 = 18,000 (1 + 0.0824/4)^4t

22,000/18,000 = (1+ 0.0206)^4t

11/9 = 1.0206^4t

 

Your variable is in the exponent, so you need to take the ln (or log) of both sides.

ln(11/9) = ln(1.0206^4t)

ln(11/9) = 4t ln(1.0206)

ln(11/9) / (4 ln(1.0206)) = t

t = 2.4603 yr

 

To find how many months this is more than 2 years, multiply the decimal part by 12

0.04603 * 12 = 5.523 mo

 

Round up because the interest won't be added until the end of the quarter:

t = 2 years, 6 months