Understanding APR, APY and Compound Interest

This is why the two are not directly comparable, and why lenders quote APR while savings institutions quote APY. Each convention happens to present its product in the more favourable light.

What APR includes

For US consumer lending, the Truth in Lending Act requires APR to include not just interest but most mandatory fees — origination charges, points on a mortgage, certain closing costs. That makes it a better comparison tool than the nominal interest rate.

A mortgage at 6.5 percent interest with two points of origination fee might carry an APR of 6.8 percent. Another at 6.7 percent with no points might carry an APR of 6.75 percent. The second is cheaper despite the higher headline rate, and only the APR reveals it.

The caveat is that APR assumes you hold the loan for its full term. If you expect to sell or refinance in five years, points paid upfront are amortised over thirty years in the APR calculation but borne entirely within your five. For short horizons, compare total costs over your actual expected period instead.

How compounding frequency changes the outcome

Compounding means earning interest on previously earned interest. The more often it happens, the higher the effective return, though the effect diminishes as frequency increases.

Ten thousand dollars at 5 percent for one year: annual compounding gives $10,500. Monthly gives about $10,511.62. Daily gives about $10,512.67. The gap between annual and monthly is meaningful; between monthly and daily, negligible. This is why the difference between two savings accounts is usually about the rate rather than the compounding schedule.

For borrowing, compounding works against you, and credit cards typically compound daily. This is part of why card debt grows faster than the nominal rate suggests.

The rule of 72

Divide 72 by the annual rate to approximate how many years until money doubles. At 6 percent, roughly twelve years. At 9 percent, eight years. At 3 percent, twenty-four.

It works in reverse for inflation: at 3 percent, prices double in about twenty-four years, meaning money held in cash loses half its purchasing power over that period. It also works for debt — a balance at 24 percent doubles in about three years if you make no payments.

Why small differences compound into large ones

Compounding is multiplicative, so differences widen over time rather than staying proportional. Ten thousand dollars over forty years at 6 percent becomes roughly $102,900. At 7 percent, roughly $149,700. One percentage point produced nearly 46 percent more money.

This is the whole argument for minimising investment fees, and it applies identically to debt. Reducing a mortgage rate by half a point saves tens of thousands over thirty years, which is why the hour spent shopping lenders pays better than almost any other hour available.

Nominal versus real returns

A 5 percent return with 3 percent inflation is roughly 2 percent real, and real return is what determines whether your purchasing power grows. Cash savings at 4.5 percent against 3 percent inflation preserve value modestly; the same savings at 0.5 percent lose value steadily.

Taxes reduce this further. Interest is taxed as ordinary income, so a 4.5 percent yield to someone in the 24 percent bracket returns about 3.4 percent before state tax and before inflation. The genuinely useful figure is after-tax real return, and it is frequently close to zero for cash.

Practical takeaways

Compare borrowing on APR and total amount repayable. Compare savings on APY. Check the compounding frequency but do not agonise over it. Use the rule of 72 for quick mental estimates.