The interest rate of the investment is: 1.42%
How to find the interest rate?
To find the interest rate required for Gabriel to end up with $570 after 15 years of compounding interest quarterly, we can use the formula for compound interest:
A = P(1 + r/n)
Where:
A = Final amount
P = Principal amount (initial investment)
r = Annual interest rate (in decimal form
n = Number of times interest is compounded per year
t = Number of years
Since we want to find the interest rate, we can rearrange the formula:
r = ( (A / P)
) ) - 1
Plugging in the given values, we have:
r = ( (570 / 440)^(1/(4*15)) ) - 1
r ≈ 0.0142
To convert the decimal form to a percentage, we multiply by 100:
r ≈ 0.0142 * 100 ≈ 1.42%
Therefore, Gabriel would require an interest rate of 1.42% in order to end up with $570 after 15 years of compounding interest quarterly.
Complete question is:
Gabriel is going to invest $440 and leave it in an account for 15 years. Assuming the interest is compounded quarterly, what interest rate, to the nearest tenth of a percent, would be required in order for Gabriel to end up with $570?