Answer to Question #115981 in Finance for Smith

Question #115981
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?
1
Expert's answer
2020-05-17T18:27:53-0400

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"









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