Solve the following by using the present value formula.
Compound Amount- $675
Term of Investment-15 months
Nominal Rate (%)- 2.7
Interest Compounded quarterly
Present Value ___________?
Compound Interest _________?
To solve this problem using the present value formula, we need to use the formula for calculating the present value of a compound amount:
PV = CV / (1 + r/n)^(nt)
Where:
PV = Present Value
CV = Compound Amount
r = Nominal Interest Rate
n = Number of times interest is compounded per year
t = Number of years
First, let's calculate the present value (PV). Given:
Compound Amount (CV) = $675
Nominal Interest Rate (r) = 2.7% (expressed as a decimal, so 0.027)
Number of times interest is compounded per year (n) = 4 (interest compounded quarterly)
Number of years (t) = 15 months / 12 months/year = 1.25 years
Using the present value formula, we can substitute the given values:
PV = $675 / (1 + 0.027/4)^(4 * 1.25)
PV = $675 / (1 + 0.00675)^(5)
PV = $675 / (1.00675)^(5)
PV = $675 / 1.0339875
PV = $653.77 (rounded to the nearest cent)
Therefore, the present value is $653.77.
To calculate the compound interest, we can subtract the present value from the compound amount:
Compound Interest = Compound Amount - Present Value
Compound Interest = $675 - $653.77
Compound Interest = $21.23 (rounded to the nearest cent)
Therefore, the compound interest is $21.23.