Interest Rate Calculator

1. Enter Present Value (PV). This is the starting amount, what you invest or borrow today. For example, a $10,000 lump sum investment or the current balance on a savings account.
2. Enter Future Value (FV). This is the target or ending amount. For a savings goal, it might be $15,000. For a loan payoff analysis, it might be the total amount repaid. FV must be larger than PV to produce a positive rate.
3. Set the Time Period in years. Use decimal values for partial years. 18 months = 1.5 years. 6 months = 0.5 years.
4. Choose Compounding Frequency. This tells the calculator how often interest compounds: annually, semi-annually, quarterly, monthly, or daily. Monthly is the most common for savings accounts and CDs. Annual is standard for most bond comparisons.
5. Read the Annual Rate. The compound annual rate is what most financial products quote as APR or APY. The Effective Annual Rate (EAR) accounts for how frequently compounding occurs and gives you a true apples-to-apples comparison across products with different compounding schedules.

Use the simple interest rate output to compare against the compound rate. Over periods longer than a year, the compound rate will always be lower than the simple rate because simple interest assumes no reinvestment of earnings.

To find an unknown interest rate, you rearrange the future value formula and solve for r. The formula differs depending on whether interest compounds or accrues simply.

Compound Interest Rate:
  r = n × [(FV / PV)^(1 / (n × t)) - 1]

Simple Interest Rate:
  r = (FV / PV - 1) / t

Effective Annual Rate (EAR):
  EAR = (1 + r/n)^n - 1

• FV = future value (ending amount)
• PV = present value (starting amount)
• n = compounding periods per year (12 for monthly, 365 for daily)
• t = time in years
• r = annual interest rate as a decimal

Worked example: You invest $10,000 and it grows to $15,000 over 5 years with monthly compounding.

r = 12 × [(15,000 / 10,000)^(1 / (12 × 5)) - 1]
r = 12 × [1.5^(1/60) - 1]
r = 12 × [1.006784 - 1]
r = 12 × 0.006784 = 0.08141 = 8.14% annual rate

EAR = (1 + 0.08141/12)^12 - 1 = 8.47%

The EAR of 8.47% is higher than the stated 8.14% because monthly compounding means interest earns interest 12 times per year. When comparing a savings account quoted at 8% compounded monthly against a bond paying 8.3% annually, the EAR tells you the savings account actually delivers more: 8.30% vs 8.30% in this case, but the math often surprises people.