Answer:
Compound Interest,I- [tex]I=P[(1+I)^{4.5}-1][/tex]
Total Amount, A- [tex]A=P(1+i)^{4.5}[/tex]
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;
[tex]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][/tex]
Hence, the compound interest after 4 1/2 years is [tex]I=P[(1+I)^{4.5}-1][/tex]
#The total amount after the same period is [tex]A=P(1+i)^{4.5}[/tex]
