Annuities and loans
Comparing loan offers
Cut through headline rates: turn fees, flat rates and different terms into one comparable number, the effective annual cost of borrowing.
24 minintermediateMembers
Learning objectives
- Calculate installments for reducing-balance and flat-rate loans
- Calculate the effective cost of a loan with upfront fees by solving for the rate with RATE
- Explain why the monthly payment and total interest mislead when terms differ
- Build a side-by-side comparison of loan offers and choose the cheapest
Two lenders offer you the same amount. One quotes 7%, the other 3.9%. The second looks almost half the price, but it may not be cheaper at all. Headline rates hide three things that change what a loan really costs:
- Fees taken upfront (admin, arrangement or processing fees) mean you receive less than you repay interest on.
- Flat rates, common for personal and car finance, charge interest on the original amount for the whole term, even though you repay it month by month.
- Different terms change the monthly payment and the total interest, which tempts borrowers to compare the wrong numbers.
The fix is the same tool you used for IRR: find the one rate that makes the cash you actually receive equal to the payments you actually make.
Reducing balance: PMT = P × r ÷ [1 − (1 + r)⁻ⁿ] Flat rate: PMT = P × (1 + f × years) ÷ n
- P
- amount borrowed
- r
- periodic rate on the outstanding balance (APR ÷ 12)
- f
- flat rate a year, charged on the original amount for the whole term
- n
- number of payments
Included with a Formula Quest membership
The rest of this lesson is for members. Members get the full lesson, including its 4 graded exercises, and every other Finance Quest lesson.