Answer:
-Ella have enough money($16,188.21) saved in six years to buy her home.
-It will take just over 10 yrs(10.24 yrs) for Ella’s account balance to exceed $20,000.
Step-by-step explanation:
#5% interest, compounded monthly, we calculate the effective annual interest rate:
[tex]i_m=(1+i/m)^m-1, m=12, i=0.05\\\\i_m=(1+0.05/12)^{12}-1\\\\i_m=0.0511619[/tex]
The principal amount is $12,000 and the desired term is 6yrs. We calculate the compounded amount after 6yrs at [tex]i_m[/tex]:
[tex]A=P(1+i_m)^6\\\\=12000(1.0511619)^6\\\\=16188.21[/tex]
Hence, Ella wont be able to make a down-payment at the end of 6 yrs since her investment of $16,188.21 <$20,000
To get how long she will be able to make the down-payment, we equate and make n the subject of the formula:
[tex]A=P(1+i)^n\\\\20000=12000(1.0511619)^n\\\\\frac{5}{3}=1.0511619^n\\\\n=\frac{log \frac{5}{3}}{log \ 0.0511619}\\\\=10.24\ yrs[/tex]
Hence, it will take just over 10 yrs for Ella’s account balance to exceed $20,000.
