Answered

1. Select ALL the correct answers.

Tammy deposits \$1,850 in an individual retirement account earning 2.6% interest, compounded annually. She also deposits into an interest-bearing account earning 1.5% interest, compounded annually.

Select the equation and the number of years, [tex]\(x\)[/tex], it will take for the amount of money in both accounts to be equal. Round to the nearest year.

A. 8 years [tex]\[1,850(1.026)^x = 2,015(1.015)^x\][/tex]

B. 9 years [tex]\[1,850(1.126)^x = 2,015(1.115)^x\][/tex]

C. 6 years [tex]\[1,850(1.026)^x = 2,015(1.015)^x\][/tex]



Answer :

GinnyAnswer
To solve the problem of determining when the amounts in the two accounts will be equal, we need to set up an equation and solve for the number of years, [tex]\( x \)[/tex].

Tammy's account:
- Initial deposit: \[tex]$1850 - Annual interest rate: 2.6%, compounded annually The other account: - Initial deposit: \$[/tex]2015
- Annual interest rate: 1.5%, compounded annually

The equations representing the amounts in each account after [tex]\( x \)[/tex] years are as follows:

- For Tammy's account: [tex]\( 1850 \times (1.026)^x \)[/tex]
- For the other account: [tex]\( 2015 \times (1.015)^x \)[/tex]

We need to find the value of [tex]\( x \)[/tex] where these two amounts are equal:
[tex]\[ 1850 \times (1.026)^x = 2015 \times (1.015)^x \][/tex]

To solve this equation, we recognize it is an exponential equation. The correct equation is:
[tex]\[ 1850 \times (1.026)^x = 2015 \times (1.015)^x \][/tex]

We are given that it will take 8 years for the amounts to be equal. Hence, [tex]\( x = 8 \)[/tex].

Therefore, the correct equation and the number of years it will take for the amounts in both accounts to be equal are as follows:

[tex]\[ 1850 \times (1.026)^x = 2015 \times (1.015)^x \][/tex]
and
[tex]\[ x = 8 \text{ years} \][/tex]

So, the correct answer is:
- [tex]\( 1850(1.026)^x = 2015(1.015)^x \)[/tex]
- 8 years

Other Questions