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Compound Interest Simplified Revision Notes

Revision notes with simplified explanations to understand Compound Interest quickly and effectively.

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Compound Interest

Compound Interest Formula

F=P(1+i)tF=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

€850 is invested for 6 years at an annual interest rate of 4.5%. Calculate the final amount and the interest earned.

i=0.045,P=850,t=6i=0.045,P=850,t=6F=850(1+0.045)6=1106.92F=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−PI=F-P1106.92−850=€256.921106.92-850=€256.92

Example

infoNote

€10,000 is borrowed for three years at an APR of 5% compounded annually. How much is owed at the end of the third year.

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

Example

infoNote

€P is invested for 8 years at a certain annual rate, giving a percentage increase in the original sum of 42.2%. What is the annual interest rate (AER), correct to one decimal place ?

The final amount F is P(1.422)

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

Divide by P.

(1.422)=(1+i)8(1.422)=(1+i)^8(1.422)18=(1+i)(1.422)^\tfrac{1}{8}=(1+i)(1.422)18−1=i(1.422)^\tfrac{1}{8}-1=i0.045=i0.045=ir=4.5%r=4.5 \%

Example

infoNote

Find the number of years it takes for €20,000 to grow to €23,152.50 when invested at 5% interest compounded annually.

F=23,152.50,P=20,000,r=0.05F=23,152.50,P=20,000,r=0.05F=P(1+i)tF=P(1+i)^t23,152.50=20,000(1.05)t23,152.50=20,000(1.05)^t

Isolate t in order to find the number of years :

23,152.5020,0000=1.05t\frac{23,152.50}{20,0000}=1.05^tlog⁡(23,152.5020,0000)=log⁡(1.05t)\log\left(\frac{23,152.50}{20,0000}\right)=\log(1.05^t)log⁡(23,152.5020,0000)=tlog⁡(1.05)\log\left(\frac{23,152.50}{20,0000}\right)=t\log(1.05)t=3t=3
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