Compound Interest Revision Notes for Leaving Cert Mathematics

Compound Interest

F=P(1+i)^t

where F is the final amount, P is the initial value, i is the interest rate and t is the time.

Example

infoNote

i=0.045,P=850,t=6

F=850(1+0.045)^6=1106.92

Subtract the present amount from the final amount to see the difference earned by the interest.

I=F-P

1106.92-850=€256.92

Example

infoNote

i=0.05,P=10,000,t=3

F=10,000(1+0.05)^3=11,576.25

Example

infoNote

The final amount F is P(1.422)

P(1.422)=P(1+i)^8

Divide by P.

(1.422)=(1+i)^8

(1.422)^\tfrac{1}{8}=(1+i)

(1.422)^\tfrac{1}{8}-1=i

0.045=i

r=4.5 \%

Example

infoNote

F=23,152.50,P=20,000,r=0.05

F=P(1+i)^t

23,152.50=20,000(1.05)^t

Isolate t in order to find the number of years :

\frac{23,152.50}{20,0000}=1.05^t

\log\left(\frac{23,152.50}{20,0000}\right)=\log(1.05^t)

\log\left(\frac{23,152.50}{20,0000}\right)=t\log(1.05)

t=3