Answer:
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;
[tex]i_m=(1+i/m)^m-1\\\\i_{12}=(1+0.13/12)^{12}-1=0.1380[/tex]
The compounded amount after 1 month is therefore:
[tex]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[/tex]
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:
[tex]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[/tex]
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:
[tex]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[/tex]
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:
[tex]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[/tex]
Hence, the principal after 20 years is $13,269.22
