Question

You invest $500 in an account that has an annual interest rate of 8%, compounded weekly for 12 years. What is the equivalent interest rate and how many times will the money be compounded? How much will you have?

Answer 1

Answer:

$i_m=8.322\%\\\\624 \ compoundings\\\\A_{12}=\ 1,304.88$

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:

$i_m=(1+i/m)^m-1\\\\\#where\\i=stated \ interest\ rate\\m=number \ of \ compoundings \ per \ year\\\\\therefore i_m=(1+0.08/52)^{52}-1\\\\=0.08322\approx 8.322\%$

Hence, the equivalent interest rate is 8.322%

-Assuming one year has 52 weeks,   the number of compoundings will be :

$=compoundings \ per \ year \times \ no \ of \ years\\\\=52\times 12\\\\=624\ compoundings$

-The investment amount after 12 years is calculated as:

$A=P(1+i_m)^n, n=number \ of \ years\\\\=500(1.08322)^{12}\\\\=1304.88$

Hence, the amount after 12 years is $1304.88