Lori gets an offer from another bank that is also paying 6% on CD’s, but is compounding interest daily. How much will the $1500 CD be worth in:

18 months?


33 months?


110.4 months?

Respuesta :

Answer:

[tex]A_{18m}=\$1641.25\\\\A_{33m}=\$1769.06\\\\A_{110.4}=2604.94[/tex]

Step-by-step explanation:

Take 1 year to be equivalent to 365 days.

-Given the rate is 6% compounded daily, we find the effective annual rate and use the new rate in our calculations:

[tex]i_m=(1+i/m)^m-1\\\\=(1+0.06/365)^{365}-1\\\\\\i_m=0.06183[/tex]

#Now use the new rate of 6.183% to calculate our compounded amount using the compound interest formula:

[tex]A=P(1+i_m)^n\\P-Principal\\i_m-effective \ rate\\\\n- years\\\\\\A_{18m}=1500(1.06183)^{18/12}=1641.25\\\\A_{33m}=1500(1.06183)^{33/12}=1769.06\\\\\\A_{110.4m}=1500(1.06183)^{110.4/12}=2604.94[/tex]