• C++ Programming for Financial Engineering
    Highly recommended by thousands of MFE students. Covers essential C++ topics with applications to financial engineering.
    Python for Finance with Intro to Data Science
    Gain practical understanding of Python to read, understand, and write professional Python code for your first day on the job. Coming soon.
    An Intuition-Based Options Primer for FE
    Ideal for entry level positions interviews and graduate studies, specializing in options trading arbitrage and options valuation models.

Calculations - Rate of Return - Investing in Stocks with Loan

S.E. Livrer

New Member
I tried to answer this question but my work feels too simple? Anything wrong here? This feels too simple? I was hoping a quantitative financier could check the math? Thanks.

Question: Suppose a bank gives Ed–
● Loan = 8,000 USD,
● Months = 24,
● Monthly interest rate = 0.30%,
● The loan must be paid back in monthly installments so Excel's PMT(.003, 24, -8000, 0) = $345.98.
● Ed's monthly salary = I. So I > $345.98.
● Tax rate = T. Of course, 0 ≤ T < 1. Then (1 – T)(Breakeven Amount) = Capital gain after tax.

1. What's the total cost of the loan?

2. Ed is thinking of using this loan to invest in stocks. Ed pays off the monthly loan installments only with his monthly employment income I. What's the rate of return for Ed to breakeven?

3. Discuss the best course of action/strategy for Ed. What should he do with this loan? Should he invest in stocks?

My answer :

Ed should just be focused on breaking even/recouping – at least – with the total cost of this loan. Is it right that the total cost of this loan is just the total amount of loan interest from stocks over 24 months ($0.003*8000*24 = $576) ? The loan principal ($8,000 USD) is repaid. so it's notpart of the cost of this loan. So Ed should not expecting stocks to make me/gain the loan principal?

Then (1 – T)(Breakeven Amount) = = 0.30%($80000)(24) = 576 USD.
So Breakeven Amount (Call this B) = 576/(1 – T). So Ed breaks even on this loan -– if and only if – Ed make 576/(1 – T) over 24 months (so the rate of return is B / (10000 + B)).