You take out a loan of $25,000 from the ABC company.It is due in 5 years with interest at j₂ = 6%.After 18 months,ABC sells your loan to the XYZ company at a price that will earn XYZ a rate of return of j₄ = 5%.What price does XYZ pay?

Question

Quizplus · Accepted Answer

First, we need to calculate the outstanding balance of the loan after 18 months. Since the loan is due in 5 years, there are 3.5 years left after 18 months:

N = 3.5 years x 2 = 7 compounding periods

The interest rate per period is:

i = 6% / 2 = 3%

Using the formula for the future value of an annuity:

FV = PMT x ((1 + i)^n - 1) / i

Where PMT is the loan payment, we can solve for FV:

$25,000 = PMT x ((1 + 3%)^7 - 1) / 3%

PMT = $3,590.62

So after 18 months, the outstanding balance of the loan is:

PV = $3,590.62 x ((1 + 3%)^18 - 1) / 3%

PV = $22,832.77

To find out how much XYZ pays for the loan, we need to calculate the present value of the remaining payments, discounted at 5% per year for 3.5 years:

N = 3.5 years x 2 = 7 compounding periods

i = 5% / 2 = 2.5%

Using the formula for the present value of an annuity:

PV = PMT x (1 - (1 + i)^-n) / i

Where PMT is the loan payment, we can solve for PV:

PV = $3,590.62 x (1 - (1 + 2.5%)^-7) / 2.5%

PV = $22,234.61

So XYZ pays $22,234.61 for the loan.

You Take Out a Loan of $25,000 from the ABC