Question

Question 19

Jon has a savings account that accumulates compound interest. The 4% annual interest rate is compounded 12 times a year. This function describes the relationship between the amount of money in the account and the number of years the account is allowed to grow.
A(t)=2000(1+0.0412)12t
Jon finds the value of A(12). Which quantity has he found?

A
the amount in the account after 12 years

B
the number of months the account has accumulated 4% interest

C
the amount in the account after 12 months

D
the number of years the account has accumulated 4% interest

Answer 1

When Jon determined A(12), it means he must have found the amount in the account after 12 years. i.e. the amount when t = 12 years.

Hence, option (A) is true.

Explanation:

BACKGROUND KNOWLEDGE ABOUT EXPONENTIAL GROWTH

We know that an exponential increase in Math can be termed as the rapid increase of an amount by percentage over a certain period of time.

It can be expressed using the formula

y = a (1+b)ˣ

here

y represents the final amount

a represents the original amount

b represents the growth factor

x represents the time that has passed

Now, let is us map our problem because it indicates the same concept.

SOLVING THE QUESTION

Given the function

`A\left(t\right)=2000\left(1+0.0412\right)^(12t)`

Here

A(t) represents the final amount

2000 represents the original amount

0.0412 represents the growth rate

t represents the number of years

Thus,

When Jon determined A(12), it means he must have found the amount in the account after 12 years. i.e. the amount when t = 12 years.

Hence, option (A) is true.