Question

Find the compound interest and the total amount after 4 years and 6 months if the interest is compounded annually

Answer 1

Answer:

Compound Interest,I- $I=P[(1+I)^{4.5}-1]$

Total Amount, A- $A=P(1+i)^{4.5}$

Step-by-step explanation:

Compound interest is the difference between the initial amount invested at time t=0and the final amount of the investment at time t.

-Let the initial amount invested be P, the annual rate be i and A be the final amount of the investment.

-Let I be the compound interest earned.

-Given that the investment term n=4yrs 6 months, the compound interest is calculated as;

$A=P(1+i)^n\\\\I=A-P\\\\\# n=4.5,P=P, i=i\\\\\therefore I=P(1+i)^{4.5}-P\\\\=P[(1+I)^{4.5}-1]\\\\I=P[(1+I)^{4.5}-1]$

Hence, the compound interest after 4 1/2 years is $I=P[(1+I)^{4.5}-1]$

#The total amount after the same period is $A=P(1+i)^{4.5}$