Question

A borrower agrees to repay a loan of $ 3000 by 15 annual repayments of $500, the first repayment being due after five years. Find the annual yield for this transaction.

Answer 1

We will assume that the annual rate is $i$. Then we have:

$500(\frac{1}{(1+i)^5}+\frac{1}{(1+i)^6}+..+\frac{1}{(1+i)^{20}})=3000$ .

we go to step two where we obtain:

$\frac{500}{(1+i)^5}\frac{(1-\frac{1}{(1+i)^{16}})}{1-\frac{1}{(1+i)}}=3000$

From it we receive:

$${(\frac{1}{(1+i)^5}-\frac{1}{(1+i)^{21}})}=6(1-\frac{1}{(1+i)})$$

Solving the latter numerically, we obtain:

$\frac{1}{(1+i)}=0.91903$

From the latter we obtain i:

$i\approx0.0881.$ Which is rounded off to 4 decimal places