Tools › Investing › Saving and Planning › Pay Off Debt or Invest › Example
300 extra a month: prepay a 6.5 % loan or invest at 7 %? Net worth of both paths and the break-even return
| Tool | Pay Off Debt or Invest |
| Source | Closed-form loan amortisation and annuity sums; Kellison, S. G. (2009). The Theory of Interest, 3rd ed. McGraw-Hill/Irwin, New York. The case is illustrative, not a printed example. |
| Level | Undergraduate |
Problem
A borrower owes 25,000 at 6.5 % a year with 60 monthly payments left and has 300 extra each month. Follow two paths for 10 years with the same monthly outlay: prepay the loan and then invest the freed payment, or invest the extra at an assumed constant 7 % a year while the loan runs its course. Find the net worth of each path, the interest and months saved by prepaying, and the investment return at which the paths end level.
Inputs to Enter
- Loan balance 25,000; loan rate 6.5 % a year charged monthly; 60 months left
- Extra 300 a month; investment return 7 % a year (constant); 10 years compared
Answers
- Monthly loan rate 0.065 / 12 = 0.005417; payment 25,000 · i (1 + i)^60 / [(1 + i)^60 − 1] = 489.15; interest if the loan runs its course 4,349.22
- Monthly outlay in both paths 489.15 + 300 = 789.15; monthly investment rate 1.07^(1/12) − 1 = 0.005654
- Prepay path: loan cleared in ln[789.15 / (789.15 − 135.42)] / ln(1.005417) = 34.85, that is month 35 with a last payment of 670.25; interest 2,501.48, a saving of 1,847.75 and 25 months
- Prepay path net worth after 120 months: 118.90 · (1 + j)^85 + 789.15 [(1 + j)^85 − 1] / j = 86,008.64
- Invest path net worth: 300 [(1 + j)^120 − 1] / j + 489.15 [(1 + j)^60 − 1] / j = 86,141.24
- Invest minus prepay 132.60 at a constant 7 % return
- Break-even return (1 + 0.005417)^12 − 1 = 6.697 % a year, the loan rate stated as growth over a year; both paths then end at 85,091.38
- Advanced mode (volatility 15 %): investing ends ahead on 45 % of 4,000 simulated lognormal return histories, a model output
Notes
The tool's default inputs are this case; press Submit. Both paths are also stepped month by month and checked against an independent numpy ledger model (test_debt_payoff_vs_invest.php). The saving from prepaying is certain and the investment return is an assumption; the page describes the two paths and does not say which to choose. A calculator for education and analysis, not investment advice.