Answer to Question #115981 in Finance for Smith

Question

Sachin has asked his flat mate Jason for a $400 loan to cover a portion of his rent and utility costs. Sachin proposes repaying the loan with $350 from each of his next two financial aid disbursements, the first 3 months from now and the second 12 months from now. Jason's alternative is to earn 4% annually in his money market account. Assume there is no risk of default, and that compounding is monthly. What is the NPV of the loan from Jason's perspective?

Answer 1

The installment paid in the first four month =

$350=p(1+\dfrac{r}{12})^t$

$350=p(1+\dfrac{4}{12})^3$

$350=p(1+0.0033)^3$

$350=1.01p$

$p=\dfrac{350}{1.01}=346.52$

The next series of installment for 10 months from first payment

$350=p(1+\dfrac{4}{12})^{15}$

$350=(1+0.0033)^{15}p$

$350=1.05066p$

$p=\dfrac{350}{1.05066}=333.124$

$\text{Present value of the loan}=333.124 +346.52$

$\text{Present value of the loan}=679.644$