A charity received a donation of $20,500, and invested it at a 6% simple interest rate.
A. How long would it take for the charity to earn $5, 535 interest?
B. What is the minimum number of full years the charity should allow the investment to mature to double the original investment?
After n years, the interest is prn. So, you want
(20500)(.06)n = 5535
n = 4.5 years
To double, you need .06n=2, or n=33.3 years
To solve this problem, we need to understand how simple interest works. Simple interest is calculated using the formula:
I = P * r * t
where:
I is the interest,
P is the principal amount (the initial investment),
r is the interest rate (expressed as a decimal),
and t is the time period (in years).
Now let's solve the given questions step by step:
A. How long would it take for the charity to earn $5,535 interest?
We know the principal amount (P) is $20,500, the interest (I) is $5,535, and the interest rate (r) is 6% or 0.06. We need to find the time period (t).
Using the formula, we can rearrange it to solve for t:
t = I / (P * r)
Substituting the given values, we get:
t = 5,535 / (20,500 * 0.06)
Calculating the expression on the right:
t = 5,535 / 1,230
t ≈ 4.5 years
Therefore, it would take approximately 4.5 years for the charity to earn $5,535 in interest.
B. What is the minimum number of full years the charity should allow the investment to mature to double the original investment?
To double the original investment, the charity needs to earn an amount equal to the principal amount (P).
Using the same formula, we can rearrange it to solve for t:
t = P / (I * r)
Substituting the given values, we have P = $20,500, I = $20,500, and r = 0.06.
t = 20,500 / (20,500 * 0.06)
Calculating the expression on the right:
t = 20,500 / 1,230
t ≈ 16.67 years
Since we cannot have partial years, the minimum number of full years the charity should allow the investment to mature to double the original investment is 17 years.