Answer:
You pay today for a $2124.7
Step-by-step explanation:
Consider the provided information,
Interest rates are 4% annually with a face value of $2,700 that matures in 6 years.
Total number of months = n = 6 × 12 = 72
Interest is 4% annually which can be written as:
i = 0.04/12 = 0.00333...
FV is $2700.
Now, use the formula:
[tex]FV = PV (1+i)^n[/tex]
Substitute the respective value in above formula.
[tex]2700= PV (1+0.0033)^{72}[/tex]
[tex]\frac{2700}{ (1+0.0033)^{72}}= PV[/tex]
[tex]\frac{2700}{ 1.27}= PV[/tex]
On solving the above equation, we get the value of PV is:
[tex] PV=2124.7[/tex]
Hence, you pay today for a $2124.7
You would pay $2130 today for a zero-coupon bond with a face value of $2,700 that matures in 6 years
The given parameters are:
Face Value (FV) = 2700
Duration (n) = 6 years
Interest rate (i) = 4%
Convert the duration to months
n = 6 × 12 = 72
Express the interest rate, monthly
i = 4%/12 = 0.0033
The future value is calculated as:
[tex]FV = PV * (1 + i)^n[/tex]
So, we have:
[tex]2700 = PV * (1 + 0.0033)^{72}[/tex]
Evaluate the sum
[tex]2700 = PV * (1.0033)^{72}[/tex]
Evaluate the exponent
[tex]2700 = PV * 1.26771[/tex]
Divide both sides by 1.26771
[tex]PV = 2129.82[/tex]
Approximate
[tex]PV = 2130[/tex]
Hence, the present value is $2130
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