About

Finding the necessary return rate to meet a financial target is a common reverse-engineering problem in finance. Whether determining the true APR of a payday loan or calculating the yield required to double an investment in five years, solving for the rate is essential. This tool isolates the variable r in standard financial equations. It handles the complexity of high-frequency compounding which significantly alters the Effective Annual Rate (APY). Accuracy is maintained using double-precision logic to prevent rounding errors common in manual estimates.

Formulas

For Simple Interest, the rate is linear.

r = A − PP × t

For Compound Interest, the formula rearranges to use roots.

r = n × nt√AP − 1

Where A is Total Amount, P is Principal, t is Time (years), and n is compounding frequency.

Reference Data

Frequency (n)	Nominal Rate	Effective Rate (APY)	Formula Concept
Annually (1)	10.00%	10.00%	r = APY
Semi-Annually (2)	10.00%	10.25%	(1+r/2)²
Quarterly (4)	10.00%	10.38%	(1+r/4)⁴
Monthly (12)	10.00%	10.47%	(1+r/12)¹²
Daily (365)	10.00%	10.52%	(1+r/365)³⁶⁵

Frequently Asked Questions

Nominal Rate is the stated interest per year without accounting for compounding. APY (Annual Percentage Yield) includes the effect of compounding, showing the true earning or cost over one year.

Often you know your starting amount (Principal) and your target goal (Total Amount), but you need to know what investment vehicle (Bond, Stock, High-Yield Savings) will provide the return needed to bridge that gap.

Continuous compounding uses Euler's number (e). It represents the theoretical limit of compounding frequency, yielding slightly higher returns than daily compounding.

Yes. If the Final Amount (A) is less than the Principal (P), the tool will output a negative percentage, indicating a loss.