Question

What is the yield to maturity​ (ytm) on a simple loan for ​$2 comma 0002,000 that requires a repayment of ​$10 comma 00010,000 in five​ years' time?

Answer 1

Answer: The YTM is 37.97%.

YTM or yield-to -maturity is that discount rate that equates the purchase price pr present value with the value that is to be received after a fixed time period (Future Price).

We use the following formula to find the YTM

`\mathbf{FV = PV (1+r)^(n)}`

Substituting the values in the equation above we get,

`\mathbf{10,000 = 2,000 (1+r)^(5)}`

We need to solve for r in the equation above to arrive at the YTM

`\mathbf{(10,000)/(2,000) = (1+r)^(5)}`

`\mathbf{5 = (1+r)^(5)}`

Taking the 5th root on both sides we get,

`\mathbf{\sqrt[5]{5} = (1+r)}`

`\mathbf{1.379729661 = (1+r)}`

`\mathbf{r = 1.379729661 -1 = 0.379729661}`