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

Assume that the annual rate is $i$. Then we have:

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

After simplifications we get:

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

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:

$i\approx0.0881.$

Answer: 0.0881(the values is rounded to 4 decimal places)