I was asked to solve this question: given a bond which grants the following cash flow (year $t$, return):
- (0, not reported)
- (1, 10)
- (2, 10)
- (3, 20)
- (4, 20)
- (5, 100)
What is the bond price in $t=3$ with flat rate of 3% per year for the entire financial operation?
Four possible choices:
- 90.71
- 113.68
- 120
- 130.23
I tried to solve with the formula of the Discounted Cash Flow but I obtained:
$$ -x+\frac{10}{1.03}+\frac{10}{1.03^2}+\frac{20}{1.03^3}=0 $$
i.e.
$$ x=37.43$$
Can someone tell me where I am wrong? Thanks in advance.
What is the bond price in $t=3$?
Try the cash flows in years $4$ and $5$ discounted back to year $3$, which in your terms means $$-x+\frac{20}{1.03}+\frac{100}{1.03^2}=0$$