Answer:
[tex]i_m=8.322\%\\\\624 \ compoundings\\\\A_{12}=\$1,304.88[/tex]
Step-by-step explanation:
#The equivalent interest rate per annum is equal to the effective interest rate.
-Given 8% compounded weekly( Take 1 yr=52 weeks) the effective interest rate is calculated as:
[tex]i_m=(1+i/m)^m-1\\\\\#where\\i=stated \ interest\ rate\\m=number \ of \ compoundings \ per \ year\\\\\therefore i_m=(1+0.08/52)^{52}-1\\\\=0.08322\approx 8.322\%[/tex]
Hence, the equivalent interest rate is 8.322%
-Assuming one year has 52 weeks, the number of compoundings will be :
[tex]=compoundings \ per \ year \times \ no \ of \ years\\\\=52\times 12\\\\=624\ compoundings[/tex]
-The investment amount after 12 years is calculated as:
[tex]A=P(1+i_m)^n, n=number \ of \ years\\\\=500(1.08322)^{12}\\\\=1304.88[/tex]
Hence, the amount after 12 years is $1304.88
Answer:
8% annual interest rate when compounded weekly =
(1 + .08/ 52)^52 = 1.00153846153846154^52 = 1.08322047419671 =
8.322047419671% equivalent interest rate
In 12 years this will be compounded 624 times
12 year Total = 500 * (1.08322047419671)^12 =
1,304.8852611583 =
1,304.89 (rounded)
