Question

(This problem can be done using either a spreadsheet or your financial calculator. In either case, show all of your work. In the case of a spreadsheet, please print out the entire spreadsheet and indicate where your answers to the various parts of this problem can be found.)

A borrower is given a choice between taking out a CPM loan for $250,000 at an interest rate of four percent (4.00%), or to pay two points and receive an interest rate of 3.75% on the loan. Both loans are for thirty (30) years.

1. What would the monthly payments be on the 4% loan?

      b.   If the borrower pays for the points upfront with a check, what will the monthly payments be?

      c.   If the borrower decides to add the points into the amount that is being borrowed, what will the monthly payments be?

      d.   Based on the effective annual yield, which of these three possibilities results in the lowest cost to the borrower?

Answer 1

Answer to a

The mathematical formula to calculate the EMI (Equated Monthly Installments) is

EMI = [P x R x (1+R)^N]/[(1+R)^N-1]

Where,

P= Principal

R= Rate of Interest ( Monthly)

N= Tenure of repayment ( In months)

By applying the above formula, the following are the figures

P = 250000, R = 4% p.a. or 0.33% p.m. N = 30 years or 360 months

EMI = [250000 x 0.33% x (1 + 0.33%)³⁶⁰] / [(1 + 0.33%)³⁶⁰-1]

EMI = 1193.54 USD

Answer to b

The interest portion is getting reduced to 3.75% by paying 2 points upfront of the borowed amount.

Upfront fee = 2% of 250000 = USD 5000

Applying the same formula as applied in answer a

EMI = [P x R x (1+R)^N]/[(1+R)^N-1]

P = 250000, R = 3.75% p.a. or 0.3125% p.m. N = 30 years or 360 months

EMI = [250000 x 0.3125% x (1 + 0.3125%)³⁶⁰] / [(1 + 0.3125%)³⁶⁰-1]

EMI = 1157.79 USD

However, to pay the upfront fee of USD 5000, we may assume that he may borrow the same @4% p.a for 30 years.

By using the same formula,EMI = [P x R x (1+R)^N]/[(1+R)^N-1]

EMI = [5000 x 0.33% x (1 + 0.33%)³⁶⁰] / [(1 + 0.33%)³⁶⁰-1]

EMI = 23.87 USD

Effectively total EMI = 1157.79+23.87

Net EMI = 1181.66 USD

Answer to c

If the borrower added the upfront fee to the Principal,(assuming the interest rate remains the same) then the loan amount would become USD 255000.

By applying the same formula as applied in answer a & b

EMI = [P x R x (1+R)]/[(1+R)^N-1]

P = 255000, R = 3.75% p.a. or 0.3125% p.m. N = 30 years or 360 months

EMI = [255000 x 0.3125% x (1 + 0.3125%)³⁶⁰] / [(1 + 0.3125%)³⁶⁰-1]

EMI = 1180.94 USD

Answer to d

Taking all the above options into consideration,

Third option would be cost effective based on the monthly EMI. As the total Effective annual cost would be USD 14171.28