Using ba 2 plus to calculate paymnet

CFA Level I
#1

Please let me know how to get answer for below question in easy manner using texas instrument ba 2 plus calculator

On June 30 of this year, a bank granted a corporation a $20 million 5-year term loan
with a floating rate of 200 basis points over Treasury Bill rates, payable quarterly. The
loan principal is to be repaid in equal quarterly installments over the term. If Treasury
Bills are expected to yield 6% for the rest of the year, how much will the corporation
pay to the bank in the last half of this year?

The answer is 2,780,000

#2

Principal payment per quarter = 20,000,000 / (5 * 4) = 1,000,000

Interest at 30 Sept = 20,000,000 * 0.08/4 = 400,000

Interest at 31 Dec = (20,000,000 - 1,000,000) *0.08/4 = 380,000

Total payments = 2 * 1,000,000 + 400,000 + 380,000 = 2,780,000

2 Likes
#3

I don’t think we could get the exact answer of 2,780,000 from the BA II plus calculator but a closed answer of $2,446,268.73

Step 1: Understand the Loan Structure

  • Principal: $20 million
  • Term: 5 years
  • Floating rate: 200 basis points (2%) over the Treasury Bill rate (6%), so the effective rate is 8% annually.
  • Repayment: Equal quarterly installments over 5 years (20 quarters).
  • Payments: Interest is calculated and paid quarterly along with principal payments.

Step 2: Calculate Quarterly Interest Rate

  • Annual interest rate: 8% (6% Treasury + 2% floating)
  • Quarterly interest rate: 8%4=2%\frac{8%}{4} = 2%48%​=2% or 0.02.

Step 3: Input into the BA II Plus

  1. ** P/Y and C/Y: You can leave these settings as default or ensure they are set to 1 for this specific calculation since we’re manually calculating periods and rates.
  • Press 2nd →P/Y → Enter 1 → Enter.
  • Press ↓ → C/Y → Enter 1 → Enter.
  1. Enter the loan details:
  • N=20N = 20N=20 (5 years × 4 quarters)
  • I/Y=2I/Y = 2I/Y=2 (quarterly interest rate)
  • PV=20,000,000PV = 20,000,000PV=20,000,000 (loan amount)
  • FV=0FV = 0FV=0 (fully repaid at the end)
  1. Compute the quarterly payment:
  • Press CPT → PMT to get the quarterly payment amount. This will give the total payment (principal + interest) per quarter.

Step 4: Calculate Payments for the Last Half of the Year

Since you are asked for the payment in the last half of the year (two quarters), multiply the quarterly payment by 2.

You should get close to the given answer of $2,780,000.

#4

#5

I don’t think we could get the exact answer of 2,780,000 from the BA II plus calculator
but a closed answer of $2,446,268.73

I can tell you where your (incorrect) answer comes from:
i) The present value of 20 EQUAL payments of x discounted at 2% per period (AND COMPOUNDED EVERY PERIOD) is
PV=x\sum_{n=1}^{20}1.02^{-n}=16.35143334x
ii) If you set the present value of that payment stream equal to 20, then
16.35143334x=20 or x=1.223134364
So each of your equal payments is 1.223134364
iii) Two of these payments would be 2x=2.446268728

I’ve just laid out what you calculated. It differs from the problem posed by the original poster.

@breadmaker showed you how to do the actual problem