What amount 18 months ago is equivalent to $2300, 1.5 year from now if money earn 7% compounded monthly during the interving time?
i know: FV=$2300 j=7% m=12 and ?n=36?
i=7%/12
PV=FV(1+i)^-n
PV=2300(1+.07/12)^-36
PV=1865.48
The answer is $1865.45
What i don't understand is how do we get the "n=36"...plz help!!!
18 months + 1.5 years = 36 months
thnx :D!!!
but im confuse because isnt n= mt
m=12
t= 18months?
To understand how we get "n=36" in this question, let's break it down step by step.
First, we need to determine the time period involved. The question states that the amount 18 months ago is equivalent to $2300, 1.5 years from now. Since 18 months is equivalent to 1.5 years, it tells us the time period over which the interest is compounded.
Next, we need to determine the number of compounding periods within that time period. The interest is compounded monthly, meaning that it is compounded 12 times a year. So, for a time period of 1.5 years, there will be a total of 1.5 * 12 = 18 compounding periods.
Now, let's compare this to the formula you mentioned: PV = FV(1+i)^(-n).
In this formula:
- PV represents the present value, which is the amount 18 months ago.
- FV represents the future value, which is the value 1.5 years from now.
- i represents the interest rate per compounding period.
- n represents the number of compounding periods.
Given that the present value (PV) is $2300 and the future value (FV) is what we're trying to find, we can rearrange the formula as follows:
PV = FV(1+i)^(-n)
FV = PV / (1+i)^(-n)
Now, we substitute the given values into the equation:
FV = $2300 / (1 + 7%/12)^(-18)
FV = $2300 / (1.00583)^(-18)
FV = $2300 / 0.9077296
Calculating this, we get FV = $2532.753.
But wait! This is the future value, not the present value we are looking for. To find the present value, we need to consider the amount 18 months ago, which is equivalent to this future value. Therefore, we need to discount the future value to find the present value.
PV = FV / (1 + i)^n
PV = $2532.753 / (1 + 7%/12)^18
PV = $2532.753 / (1.00583)^18
PV = $2532.753 / 1.2100977
Calculating this, we get PV = $2091.58.
Therefore, the present value 18 months ago that is equivalent to $2300 in 1.5 years is approximately $2091.58.