Simple vs Compound Interest

Simple interest is a fixed percent of the original amount (the principal) for each year:

P is the principal, r is the yearly rate as a decimal, and t is the time in years. $5,000 at 4% for 3 years:

The total, or amount, is the principal plus the interest: $5,600. The interest is the same $200 every year.

The rate is per year, so the time must be in years too:

• Months: divide by 12. $1,200 at 6% for 18 months is 1,200 × 0.06 × 1.5 = $108.
• Days: divide by 365. $20,000 at 3.5% for 90 days is 20,000 × 0.035 × 90 ÷ 365 = $172.60.
• Some banks use a 360-day year ("banker's interest"), which gives $175.00 for the same loan.

• Rate = I ÷ (P × t). $5,000 earning $600 in 3 years: 600 ÷ 15,000 = 0.04, so 4%.
• Time = I ÷ (P × r). $5,000 at 4% earns $200 a year, so $1,000 takes 5 years.
• Principal = A ÷ (1 + r × t). To have $5,600 in 3 years at 4%, start with 5,600 ÷ 1.12 = $5,000.

With compound interest, each year's interest is added to the balance, and next year's interest is worked out on the bigger number:

$5,000 at 4% compounded yearly for 3 years: 5,000 × 1.04 × 1.04 × 1.04 = $5,624.32, which is $24.32 more than simple interest. Year by year: $200, then $208, then $216.32 of interest.

Interest can also compound monthly or daily, which adds a little more. Savings accounts show this as the APY.

$10,000 at 5%:

• After 5 years: simple $12,500, compound $12,763
• After 10 years: simple $15,000, compound $16,289
• After 20 years: simple $20,000, compound $26,533
• After 30 years: simple $25,000, compound $43,219

For the first few years the two are close. Over decades, compound interest pulls far ahead, which is why it matters so much for retirement savings, and for debt that you don't pay off.

• Simple interest doubles your money in exactly 100 ÷ rate years. At 5%, that's 20 years.
• Compound interest doubles it in about 72 ÷ rate years (the rule of 72). At 5%, that's about 14.4 years.

The rule of 72 is a quick estimate that works best for rates between about 4% and 12%.

• Simple interest: short-term loans, some car and personal loans, and bond coupon payments.
• Compound interest: savings accounts, CDs, credit card balances and investments.

As a borrower, you want less compounding; as a saver, more. Compare loans by APR and savings by APY, which already account for how often interest is added.

Check your answers with the Simple Interest Calculator.

1. $2,000 at 5% simple interest for 4 years
   Show answer

   $400 interest, $2,400 total
2. $3,000 at 6% for 8 months
   Show answer

   $120. 3,000 × 0.06 × 8 ÷ 12.
3. $1,000 grows to $1,150 in 3 years with simple interest. What's the rate?
   Show answer

   5%. 150 ÷ (1,000 × 3).
4. $4,000 at 5% compounded yearly for 3 years
   Show answer

   $4,630.50. 4,000 × 1.05³.
5. How long to double money at 8%, simple vs compound?
   Show answer

   Simple: 12.5 years (100 ÷ 8). Compound: about 9 years (72 ÷ 8).
6. After 10 years, which is more: $5,000 at 6% simple, or $5,000 at 5% compounded yearly?
   Show answer

   Compound: $8,144.47 vs $8,000, despite the lower rate.