Final answer:
To find the interest rate required for an $8500 investment to triple in 5 years when compounded monthly, we can use the formula: A = P(1 + r/n)^(nt). Plugging in the values, we find that an interest rate of approximately 9.54% compounded monthly is required for the $8500 investment to triple in 5 years.
Step-by-step explanation:
To find the interest rate required for an $8500 investment to triple in 5 years when compounded monthly, we can use the formula:
A = P(1 + r/n)^(nt)
where:
- A = final amount
- P = principal amount
- r = annual interest rate (expressed as a decimal)
- n = number of times interest is compounded per year
- t = number of years
In this case, P = $8500 and A = $8500 * 3 = $25500. Let's assume the interest rate is 'r' and the compounding frequency is 'n = 12' (monthly).
Plugging in the values, we get:
$25500 = $8500(1 + r/12)^(12*5)
Solving for 'r', we have:
(1 + r/12)^(60) = 3
To find the value of 'r', we need to take the 60th root of both sides:
(1 + r/12) = 3^(1/60)
Simplifying, we have:
1 + r/12 = 1.079460507 = 1.0795
Subtracting 1 from both sides, we get:
r/12 = 0.0795
Multiplying both sides by 12, we have:
r = 0.954
Therefore, an interest rate of approximately 9.54% compounded monthly is required for the $8500 investment to triple in 5 years.