Michaela D. answered • 08/09/22

Experienced Middle/High school tutor specializing in STEM subjects

**A = P(1 + r/n)**^{nt}

A = Accrued amount (principal + interest)

P = Principal amount

r = Annual nominal interest rate as a decimal

R = Annual nominal interest rate as a percent

r = R/100

n = number of compounding periods per unit of time

t = time in decimal years; e.g., 6 months is calculated as 0.5 years. Divide your partial year number of months by 12 to get the decimal years.

I = Interest amount

**A total of $12,000 is invested at an annual rate of 9%. Find the balance after 5 years if it is compounded**

a) quarterly

A = 12000( 1+ .09/4)^{4*5}

A = 12,000(1 + 0.0225)^{(20)}

A = $18,726.11

A = P + I where

P (principal) = $12,000.00

I (interest) = $6,726.11

b) continuously

A = Pe^{rt}

A = 12,000(2.71828)^{(0.09)(5)}

A = $18,819.75

A = P + I where

P (principal) = $12,000.00

I (interest) = $6,819.75