Question

what is yield to maturity on simple loan for $1000000that requires a payment of $2000000 in five 7 years time?

Answer 1

To calculate the Yield to Maturity (YTM) on a simple loan, you would typically use the formula for the present value of a future amount. The YTM is the interest rate \( r \) that makes the present value of the loan payments equal to the loan amount.

In this case, you have:

- Present Value (PV) = $1,000,000 (the loan amount)
- Future Value (FV) = $2,000,000 (the amount to be paid in the future)
- Time (t) = 7 years

The formula for the present value is:

\[
PV = \frac{FV}{(1 + r)^t}
\]

Rearranging that equation to solve for the yield \( r \):

\[
(1 + r)^t = \frac{FV}{PV}
\]

\[
1 + r = \left( \frac{FV}{PV} \right)^{\frac{1}{t}}
\]

\[
r = \left( \frac{FV}{PV} \right)^{\frac{1}{t}} - 1
\]

Now plugging in the numbers:

\[
r = \left( \frac{2,000,000}{1,000,000} \right)^{\frac{1}{7}} - 1
\]

\[
r = (2)^{\frac{1}{7}} - 1
\]

Calculating \( (2)^{\frac{1}{7}} \):

\[
(2)^{\frac{1}{7}} \approx 1.1041
\]

Then,

\[
r \approx 1.1041 - 1 \approx 0.1041
\]

Which converts to a percentage:

\[
r \approx 10.41\%
\]

So, the Yield to Maturity (YTM) for this loan is approximately **10.41%** per year.