Question

After how many years will an investment of $100 compounded quarterly at 6% annually be worth $450? (round to the nearest year)

Answer 1

The investment will be worth $450 after 25.255 years which is about 25 years and 3 months.

Explanation:

You have to use the following formula to calculate the number of years:

t=ln(A/P) / n(ln(1 + r/n)), where:

t=time in years

A=Accrued amount=450

P=Principal amount=100

n=number of compounding periods per time period=4

r=interest rate=0.06

Now, you can replace the values in the formula:

t=ln(450/100)/4(ln(1+(0.06/4)))

t=ln(4.5)/4(ln(1.015))

t=1.50/0.059

t=25.255

According to this, the answer is that the investment will be worth $450 after 25.255 years which is about 25 years and 3 months.