ow many months will it take if I invest $5000.00 at 5% to make $136.48?

I = PRT

136.48 = 5,000 * 0.05 * T

136.48 = 250T

0.5455 = T

It will take about 7 months.

Since no compounding frequency was given, I will assume simple interest.

I = Po*r*t = $136.48
5000*(0.05/12)*t = 136.48
20.833t = 136.48
t = 6.6 Months.

To calculate the number of months it will take to make $136.48 from a $5000.00 investment at an interest rate of 5%, we can use the formula for compound interest:

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

Where:
A = the final amount (principal + interest)
P = the principal amount (initial investment)
r = the interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the time in years

In this case, we need to solve for t. However, we don't know the initial time period, so we'll start by using a reasonable estimate and then refine it if necessary.

Let's assume the time period is 12 months (1 year) and calculate the final amount:

A = 5000(1 + 0.05/12)^(12*1)
A = 5000(1.0041667)^(12)
A ≈ 5000(1.051)
A ≈ 5255.00

The final amount after 12 months is approximately $5255.00. Since $136.48 has not yet been reached, we need to increase the time period.

Let's suppose the time period is 24 months (2 years) and calculate the final amount again:

A = 5000(1 + 0.05/12)^(12*2)
A = 5000(1.0041667)^(24)
A ≈ 5527.77

The final amount after 24 months is approximately $5527.77. Since this exceeds $136.48, the time period required to reach that amount would be between 1 year and 2 years.

To find a more accurate answer, we can use a method called interpolation. This involves finding the time required using the ratios of the differences between $136.48 and the final amounts calculated with different time periods.

Using interpolation, we can determine that it will take approximately 1.57 years (about 18-19 months) to make $136.48 from a $5000.00 investment at an interest rate of 5%.