Simple interest

Simple interest is the amount borrowed, times the yearly rate, times the time in years: I = P × r × t.

Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.

What it is for

A supplier extends 10,000 for nine months at 6% a year, and the owner needs the cost of that before agreeing. Or an invoice is 45 days late and the contract charges interest. Either way it is one multiplication, with the time in years.

How to think about it

Write the three numbers. Turn the rate into a decimal and the time into years before multiplying. Interest plus the amount borrowed is what goes back.

Worked example

Borrow 10,000 at 6% per year for 9 months

Principal, rate, time.

t = 9 / 12 = 0.75 years

The time, in the unit the rate is quoted in.

Interest = 10,000 × 0.06 × 0.75 = 450

Principal times rate times time.

Repay = 10,000 + 450 = 10,450

What goes back at the end.

Your turn

8,000 at 5% per year for six months gives 200 of interest. Write the line with the time filled in.

Interest = 8,000 × 0.05 ×  = 200

The trap

Using months where the rate wants years. 10,000 × 0.06 × 9 is 5,400, which is a nine-year loan, not a nine-month one.

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