Seth, Tori, and Uwe each borrow $6000 for 6 years at 6% interest compounded semi

Question

Seth, Tori, and Uwe each borrow $6000 for 6 years at 6% interest compounded semi-annually. Seth makes no payments until the sixth year when he pays all the principal and interest in one lump sum. Tori pays interest only, that is she pays the accumulated interest every 6 months, and then pays the principal back at the end of the sixth year. Uwe pays back the loan with 6 level payments of X at the end of each year.

a) What is X?

b) How much interest do each of them pay? (i.e how much more than the $6000 they borrowed does each of them pay over the lifetime of the loan?)

Explanation / Answer

a. Computation of X

Effective interest rate = (1.03)^2 - 1 = 6.09%

X = Loan Amount / PVAF ( 6.09%, 6)

X = 6000 / 4.90345

X = $1223.63

b. Computation of Interest paid by each individual

1. Interest of Seth = Principal * (1+r)^n - principal

Interest of Seth = 6000 * (1+0.03)^12 - 6000

Interest of Seth = 8554.57 - 6000

Interest of Seth = $2554.57

2. Interest of Tori = Principal * 3% * 12

Interest of Tori = 6000 * 3% * 12

Interest of Tori = $2160

3. Interest of Uwe = Yearly payment * 6 - Principal

Interest of Uwe = 1223.63 * 6 - 6000

Interest of Uwe = $1341.77

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.