What is the present value of $5,000 due in ten years assuming money grows according to compound interest and the annual effectiv
1 answer:
Answer:
$ 3,085
Explanation:
Given that;
The present value(PV) ------ ???
Future payment (F) ---- $5,000
The annual effective rate are 4%, 5% and 5.5% respectively, which can be illustrated as;
r = 0.04, 0.05 and 0.055 respectively.
The present value formula is given as:
PV = 5000 × (1.04)⁻³(1.05)⁻²(1.055)⁻⁵
= $ 3,084.814759
≅ $ 3,085
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Answer:
Answer is explained in the explanation section below.
Explanation:
It's necessary to remember that the value of fixed-rate bonds is inversely proportional to the level of interest rates. The value of the bond decreases as interest rates rise; moreover, the value of the bond rises as interest rates fall. A Bond with a lower coupon sells for less than its face value. When the going rate of interest is higher than the coupon rate, this condition arises. The value of the asset would increase over time. A higher coupon bond is one that sells for a higher price than its face value. When the going rate of interest is lower than the coupon rate, this condition arises. Its value will gradually decrease until it reaches its maturity value. A par value bond that sells at par, with a coupon rate equal to the current interest rate. The coupon is usually set at the going market rate on the day the bond is sold, so it sells at par at first.
Calculations:
C = Coupon Payments = $60 (Par Value x Coupon Rate)
n = number of years = 10
i = market rate or required yield = 7% = 0.007
K = number of coupon payments in 1 year = 1
P = value at maturity or par value = 1000
Present value of ordinary annuity formula:
Bond Price = C/k * +
Just plug in the values and you will get:
Bond Price = 60 x 7.02 + 508.35
Bond Price = 421.41 508.35
Bond Price = $929.76
Similarly,
Data:
C = Coupon Payments = $60 (Par Value x Coupon Rate)
n = number of years = 10
i = market rate or required yield = 7% = 0.007
K = number of coupon payments in 1 year = 2
P = value at maturity or par value = 1000
Present value of ordinary annuity formula:
Bond Price = C/k * +
Just plug in the values and you will get:
Bond Price = 30 x 14.21 + 502.57
Bond Price = 426.37 + 502.57
Bond Price = $928.94
Answer:
$4,420.35
Explanation:
Bond Price =
Where:
- C = Coupon
- r = Yield to Maturity
- n = compounding periods to maturity
Now we plug the amounts into the formula =