INTEREST RATE FORMULAS The following slides are examples of problems that use different Interest Rate Formulas

EXAMPLE 1 P = $20 r = 7.99%= .0799 T = 2 years n = Daily = 365 Use the Order of Operations to simplify A = 20(1+.0799/365)365(2) Plugged-in the values A = 20(1+0.000218904)365(2) Simplify the Parenthesis A = 20(1.000218904)365(2) Simplify the Parenthesis A = 20(1.000218904)730 Simplify the Exponents A = 20(1.173255581) Multiply A = $23.47 Final amount to two decimal places EXAMPLE 1

P = $50 R = 14.99%=.1499 T = 4 years N = Daily VS N = Yearly EXAMPLE 2

P = $500 R = 10% =.10 T = 4 years N = Weekly Try on your own

In Nature: Something that is growing instantaneously (every instant), like snowball rolling downhill, temperature, radioactive decay. Continuous

P = $1, R = 100%, T = 1 Year Using A = P(1 + r/n)nt ‘n’ value Final Amount Annually (1) $2 Monthly (12) $2.613035 Daily (365) $2.714567 Hourly (8760) $2.718126 Minutely (525600) $2.718279 Secondly (31536000) $2.718281 2.7182818284590452353602874713527 ‘e’ = Euler’s number

EXAMPLE 3 P = $20 r = 7.99%= .0799 T = 2 years e = 2.718281828… Use the Order of Operations to simplify A = 20(e).0799(2) Plugged-in the values A = 20(e)(.1598) Simplify the Parenthesis A = 20(1.173276192) Simplify the Exponents A = 23.46552385 Multiply A = $23.47 Final amount to two decimal places EXAMPLE 3

P = $1000 e = 2.7182818 R = 25% =.25 T = 4 years Try on your own

You invest $2000 in a bank account that has a 5% annual interest rate, compounded continuously. How much will you have in 5 years? Try one more