Financial
Flat add-on interest versus annual cash-flow IRR: a four-payment example
Compare four end-of-year flat-interest payments with a declining-balance loan and calculate the annual IRR of the cash flows.
Use the actual payment timing when comparing rates
This fictional example advances 10000 at time zero and takes four equal payments at the end of years 1 through 4. A 6% annual flat rate gives total interest 2400 and annual payment 3100. The corresponding annual cash-flow IRR rounds to 9.20%.
At a 6% declining-balance annual rate, PMT gives about 2885.91 per year. Calculations use unrounded payments internally; rounding actual installments to cents can require a final-payment adjustment.
IRR is a rate per equally spaced cash-flow interval, annual only because this example uses annual intervals. It is not a universal statutory APR/GPR disclosure calculator: fees, payment dates and applicable disclosure conventions matter. Monthly payments require a different cash-flow schedule and appropriate annualization.
The helper column contains exactly four repayments. B4 must stay 4; changing the term without resizing the schedule would yield an incorrect rate. Inputs require positive principal and a nonnegative flat rate.
| Loan Comparison Metric | Formula / Cash Flows | Quoted "6%" 4-Yr $10k Loan | Borrower Impact |
|---|---|---|---|
| Add-On Annual Payment | B2 * (1 + B3 * B4) / B4 | 10,000 * 1.24 / 4 = $3,100.00 | $2,400 total interest |
| True 6% Actuarial Payment | PMT(B3, B4, -B2) | $2,885.91 / yr | $1,543.65 total interest |
| Annual cash-flow IRR | IRR(C2:C6) | About 9.20% | Annual intervals; no fees |
Four-payment flat-interest installment
Computes flat add-on installment (Principal + Principal * r_flat * Years) / Periods.
=IF(COUNT(B2:B4)<>3,"Invalid inputs",IF(OR(B2<=0,B3<0,B4<>4),"Invalid inputs",ROUND((B2 * (1 + B3 * B4)) / B4, 2)))Annual IRR for the displayed four-payment schedule
C2 is positive principal; C3:C6 are unrounded negative payments. ROUND affects the displayed IRR only. Keep these helper formulas intact.
=IF(COUNT(B2:B4)<>3,"Invalid inputs",IF(OR(B2<=0,B3<0,B4<>4),"Invalid inputs",ROUND(IRR(C2:C6), 4)))Try the example
Use the original values or change them to test your understanding.