Respuesta :
Answer:
Option D
Step-by-step explanation:
Given question is incomplete; here is the complete question.
Asako deposits $1000 into a bank that pays 1.5% interest compounded annually. Which inequality can she use to determine the minimum time in years 't' she needs to wait before the value of the account is 20% more than its original value?
A. 1000 . 1.01t > 1200
B. 1000 . 1.01t > 1.2
C. [tex]1.015^t>1200[/tex]
D. [tex]1.015^t>1.2[/tex]
Formula to get the final amount by compounding is,
Final amount = [tex]\text{Initial amount}\times(1+\frac{r}{n})^{nt}[/tex]
Here, r = rate of interest
n = number of compounding in a year
t = Time or duration of investments (In years)
Initial amount = $1000
Final amount = 20% more than its original value = $(1000 + 0.2×1000) = $1200
r = 1.5% = 0.015
Inequality that represents the final amount 20% more than the initial value,
[tex]1000(1+\frac{0.015}{1})^{1\times t}[/tex] > 1200
[tex]1.015^t[/tex] > 1.2
Therefore, Option D will be the correct option.
