Question

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

Answer 1

Compound Interest,I-
`I=P[(1+I)^(4.5)-1]`

Total Amount, A-
`A=P(1+i)^(4.5)`

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)`