Question

Asako deposits $1000 into a bank account 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?

Answer 1

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. $1.015^t>1200$

D. $1.015^t>1.2$

Formula to get the final amount by compounding is,

Final amount = $\text{Initial amount}\times(1+\frac{r}{n})^{nt}$

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,

$1000(1+\frac{0.015}{1})^{1\times t}$ > 1200

$1.015^t$ > 1.2

Therefore, Option D will be the correct option.