Question

If you invest $500 at 1.15% compounded quarterly, how many years (to the nearest hundredth) does it take for your investment to grow to $1,250?

a) 31.33 years
b) 35.98 years
c) 38.26 years
d) 40.14 years

Answer 1

To solve this problem, we can use the formula for compound interest: A = P(1 + r/n)^(nt). Plugging in the given values, the number of years required for the investment to grow to $1,250 is approximately 38.26 years.

Step-by-step explanation:

To solve this problem, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (initial investment), r is the annual interest rate (in decimal form), n is the number of compounding periods in a year, and t is the number of years. In this case, the principal is $500, the annual interest rate is 1.15% (or 0.0115 as a decimal), the compounding is quarterly (so 4 periods in a year), and the final amount is $1,250. We can plug these values into the formula to find the number of years:

A = 500(1 + 0.0115/4)^(4t) = 1250

1250/500 = (1 + 0.0115/4)^(4t)

2.5 = (1 + 0.002875)^4t

Take the natural log of both sides to solve for t:

ln(2.5) = ln(1 + 0.002875)^4t

ln(2.5) = 4t * ln(1 + 0.002875)

t = ln(2.5) / (4 * ln(1 + 0.002875))

t ≈ 38.26 years (to the nearest hundredth)