ind the present value of a payment §200 at the end of 5th year under theforce of interest 9.00% per annum.
Question
Find the present value of a payment §200 at the end of the 5th year under the force of interest 9.00% per annum.
Solution
To find the present value of a future payment, we use the formula for present value which is:
PV = FV / (1 + r)^n
where:
- PV is the present value
- FV is the future value
- r is the interest rate
- n is the number of periods
In this case, the future value (FV) is $200, the interest rate (r) is 9% or 0.09 (expressed as a decimal), and the number of periods (n) is 5 years.
So, substituting these values into the formula, we get:
PV = 200 / (1 + 0.09)^5
Now, calculate the denominator (1 + 0.09)^5 = 1.53862 approximately.
Then, divide the future value by this number:
PV = 200 / 1.53862 = $130.01 approximately.
So, the present value of a payment of 130.01.
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