Mathematics: PLEASE HELP PLEASE!! I ATTACHED A PICTURE

a. $1010.83b.$1066.77c. $1138.00d.$13,269.22Step-by-step explanation:Given the annual rate as 13%(compounded monthly) and the principal amount as $1000.a. #first we calculate the effective annual rate;The compounded amount after 1 month is therefore:Hence, the principle after one month is $1010.83b. The principal after 6 months:-From a above we have the effective annual rate as 0.1380 and our time is 6 months:Hence, the principal after 6 months is $1066.77c.The principal after 1 year:-From a above...

PLEASE HELP PLEASE!! I ATTACHED A PICTURE

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pickettkunisha14

13.05.2021

Mathematics

a. $1010.83

b.$1066.77

c. $1138.00

d.$13,269.22

Step-by-step explanation:

Given the annual rate as 13%(compounded monthly) and the principal amount as $1000.

a. #first we calculate the effective annual rate;

$i_m=(1+i/m)^m-1\\\\i_{12}=(1+0.13/12)^{12}-1=0.1380$

The compounded amount after 1 month is therefore:

$P_1=P(1+I_m)^n, n=1/12, i_m=0.1380, P=1000\\\\P_1=1000(1+0.1380)^{1/12}\\\\P_1=1010.83$

Hence, the principle after one month is $1010.83

b. The principal after 6 months:

-From a above we have the effective annual rate as 0.1380 and our time is 6 months:

$P_{6m}=P(1+i_m)^n, \ n=6m, P=1000, i_m=0.1380\\\\P_{6m}=1000(1+0.1380)^{6/12}\\\\=1066.77$

Hence, the principal after 6 months is $1066.77

c.The principal after 1 year:

-From a above we have the effective annual rate as 0.1380 and our time is 12 months:

$P_{1y}=P(1+I_m)^n, n=1/12, i_m=0.1380, P=1000\\\\P_{1y}=1000(1+0.1380)^{12}\\\\P_{1y}=1138$

Hence, the principal after 1 year is $1138.00

d. The principal after 20years:

-From a above we have the effective annual rate as 0.1380 and our time is 20yrs:

$P_{20y}=P(1+I_m)^n, n=1/12, i_m=0.1380, P=1000\\\\P_{20y}=1000(1+0.1380)^{12}\\\\P_{20y}=13269.22$

Hence, the principal after 20 years is $13,269.22

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PLEASE HELP PLEASE!! I ATTACHED A PICTURE

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