Henry invests $5,000 in a mutual fund with an annual interest rate of 7.5%. He also has a 4-yr, $10,000 loan at 3.75%. When will the amount of interest earned on the mutual fund be equal to the amount of interest paid on the loan?

Loan: $10,000 @ 3.75% for 4 years.

Pt = (Po*r*t) / (1 - (1+r)^-t.

r = (3.75% / 12)/100% = 0.003125 =
monthly % rate express as a decimal.

t = 4yrs * 12mo/yr = 48mo.

Pt=(10,000*0.003125*48)/(1-(1.003125)^-48.
Pt = 10784.33.

Int. = 10,784.3 - 10000 = 784.33.

Investment: $5,000 @ 7.5%.

Int. = 5000 * 0.075t = 784.33,
375t = $784.33,
t = 2.09yrs = 25mo.

Ah, the never-ending battle of interest rates! Well, let's crunch some numbers and bring some humor into the equation.

First, let's calculate how much interest the mutual fund will earn. We'll use the good old compound interest formula:

A = P(1 + r/n)^(nt)

Where:
A = the amount after time t
P = the principal investment
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years

So, for Henry's mutual fund investment, we have:
P = $5,000
r = 7.5% or 0.075 (in decimal form)

Now, let's find out how long it takes for the interest earned on the mutual fund to equal the interest paid on the loan.

Since we know that the loan amount is $10,000 and the interest rate is 3.75%, we can use the simple interest formula:

I = Prt

Where:
I = interest earned (or paid)
P = principal amount (loan amount)
r = interest rate (in decimal form)
t = time (in years)

In this case, we want the interest earned on the mutual fund to be equal to the interest paid on the loan. This means:

(Principal amount of the mutual fund) x (Annual interest rate of the mutual fund) x (Time of the mutual fund) = (Loan amount) x (Annual interest rate of the loan) x (Time of the loan)

5000 * 0.075 * t = 10000 * 0.0375 * 4

Now, let's solve this equation using some humorous algebra skills:

375t = 1500

t = 1500/375

t = 4

So, it would take 4 years for the interest earned on the mutual fund to be equal to the interest paid on the loan. Ah, the sweet balance of finances!

To determine when the amount of interest earned on the mutual fund will be equal to the amount of interest paid on the loan, we need to calculate the interest for both the mutual fund and the loan separately.

Let's start with the mutual fund:
The formula to calculate the interest earned on the mutual fund is:
Interest = Principal * Rate

Given:
Principal (P) = $5,000
Rate (R) = 7.5% = 0.075 (decimal form)

Interest on the mutual fund = P * R
Interest on the mutual fund = $5,000 * 0.075
Interest on the mutual fund = $375

Now let's calculate the interest paid on the loan:
Again, using the formula to calculate the interest:
Interest = Principal * Rate

Given:
Principal (P) = $10,000
Rate (R) = 3.75% = 0.0375 (decimal form)

Interest on the loan = P * R
Interest on the loan = $10,000 * 0.0375
Interest on the loan = $375

Now that we know both the interest earned on the mutual fund and the interest paid on the loan are both $375, we need to determine how many years it will take for them to be equal.

Since the interest rate on the mutual fund is fixed at 7.5% annually, and the interest rate on the loan is fixed at 3.75% annually, the interest earned on the mutual fund will always be twice the interest paid on the loan.

Therefore, the interest earned on the mutual fund will never be equal to the interest paid on the loan.

To determine when the amount of interest earned on the mutual fund will be equal to the amount of interest paid on the loan, we need to find the time it takes for the interest earned on the mutual fund to equal the interest paid on the loan.

Let's start with the interest earned on the mutual fund:
Interest = Principal × Rate × Time

Henry invests $5,000 in a mutual fund with an annual interest rate of 7.5%. Therefore, the interest earned on the mutual fund can be calculated as:
Interest Earned = $5,000 × 0.075 × Time

Now, let's calculate the interest paid on the loan:
Interest = Principal × Rate × Time

Henry has a 4-year loan with a principal of $10,000 and an annual interest rate of 3.75%. Thus, the interest paid on the loan can be calculated as:
Interest Paid = $10,000 × 0.0375 × 4

Now, we need to set up an equation to find the time when the interest earned will be equal to the interest paid:
$5,000 × 0.075 × Time = $10,000 × 0.0375 × 4

Simplifying the equation:
0.375 × Time = 0.15 × 4
0.375 × Time = 0.6

To find the time (in years), we can divide both sides of the equation by 0.375:
Time = 0.6 ÷ 0.375

Calculating:
Time = 1.6

Therefore, the time it takes for the interest earned on the mutual fund to be equal to the interest paid on the loan is 1.6 years.