If I wanted to calculate how the number of years it takes to save x number of dollars, How will I do so. I have the PV,FV and the interest rate.
Can you also tell me what 1n is in the following formula:
ln(FV / PV) / ln(1 + r)
To calculate the number of years it takes to save a certain amount of money, you can use the formula for the number of periods (n) of compound interest. The formula is:
ln(FV / PV) / ln(1 + r)
Where:
- FV is the future value or the desired amount you want to save
- PV is the present value or the current amount of money you have
- r is the interest rate per period
To calculate the number of years, you would substitute the known values for FV, PV, and r into the formula, and solve for n.
Now, regarding your second question: 1n in the formula represents the natural logarithm function. It indicates that the logarithm you're taking is with respect to the base of Euler's number (approximately 2.71828). The notation "ln" is commonly used to express the natural logarithm function, whereas "log" typically refers to the logarithm function with a base of 10.
In the given formula, we use the natural logarithm twice: once to calculate the ratio of FV to PV (ln(FV / PV)) and once to calculate the denominator (ln(1 + r)). Dividing these two values gives you the result of the logarithmic calculation, representing the number of periods or years required to reach the desired future value.