Economics Question

[Hosnon]

I'm looking for an equation to help me solve the following problem:

Assume that a person has $100,000 worth of student loan debt with a 5% interest rate. Now assume that the person gets a windfall of $100,000. Finally, assume the person can invest the windfall with a 5% rate of return. What is the best balance between paying of the debt right away and investing the windfall and paying monthly payments on the debt, partly with the interest from the investment?

These numbers were chosen randomly and I'm not really looking for the best solution...only the equation.

I'm primarily looking for that equation that can be graphically plotted so I can visually see the relationships.

Thanks!

[Pierre.Suave]

1. It looks to me that

it is a 1:1 relationship and there is no best option other than paying it off immediately.

[Hosnon]

2. What if the interest rates/sums are not equal?

I assume the graph would cross the x-axis with the sums I've listed but what does the rest of the graph look like?

[speedoo]

3. I'm very rusty on this, but...

the equation, or formula you are looking for is referred to as "Net Present Value" (NPV) or "Return on Investment" (ROI).

It's not at all complicated... the equation seeks to compare future and current cash flows (positive or ngative) by bringing them into their present value.

Try google for the terms I mentioned to find the formula. I don't have it handy.

[TahitiNut]

4. Interest expense is not tax-deductible. Interest income IS taxable.

It's better to pay off the debt when the interest income, minus taxes, is not greater than the interst expense.

[FormerDittoHead]

5. Some considerations...

First off, is the 5% NET of taxes? If you're getting 5%, but have to pay taxes on that, then the exchange is not a wash.

But RISK is the key factor here.

YOUR DEBT IS A SURE THING. Only if you're making a NET 5% on gov't insured funds would it be a wash. Say you invest in 8% corporate bonds (which should net 5%), say GE - that's not going anywhere, right?

WHO KNOWS? The FACT is that businesses *DO* go out of business. If GE goes out of business, you will STILL owe for the student loan!

Actually, I would say you could SAFELY invest in GE bonds, but my point here is that, at the very least, you should be aware of the RISK.

This does not, of course, include in/deflation or opportunity loss...

[papau]

7. all excellent points - I'd add liquidity needs - this is the cheapest cash advance he will get - so

does he anticipate a future need that will require borrowing?

[0rganism]

6. y = P*e^(i*t)

where y is total $, P is principal, i is interest rate, t is time

so after 5 years at 5% annual, $100k becomes
y = $100000(e^(.05/year * 5 years)) = $100000(1.28) = $128000

you can set different interest rates in i and compare the result on a decent graphing program