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Mekhi just graduated college and is starting his first job. He is investing money into a savings account to plan for retirement. He has $15,000 to invest in a savings account with a 3.25% APR.

6. Write an equation that models Mekhi's savings account.
7. Write the equation in slope-intercept form.
8. y-value-
slope-
9. How much money will be in the savings account if Mekhi wants to retire 30 years
later?
10. How many years would Mekhi have to work to retire with $35,000?

Mekhi just graduated college and is starting his first job. He is investing money-example-1
User Ccarton
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1 Answer

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Answer:

6. The equation that models Mekhi's savings account is:

A = P(1 + r/n)^(nt)

Where:

A = the amount of money in the account after t years

P = the initial investment ($15,000 in this case)

r = the annual interest rate (3.25% or 0.0325 as a decimal)

n = the number of times interest is compounded per year (usually 12 for monthly compounding)

t = the number of years

7. To write the equation in slope-intercept form, we need to simplify it:

A = P(1 + r/n)^(nt)

A = $15,000(1 + 0.0325/12)^(12t)

A = $15,000(1.00271)^(12t)

A = $15,000(1.00271)^12 * (1.00271)^t

A = $15,000(1.34685)^(t)

This is in exponential form, so there is no y-intercept or slope.

8. y-value: A, the amount of money in the account after t years

slope: There is no slope in an exponential equation.

9. To find out how much money will be in the savings account after 30 years:

A = $15,000(1.34685)^30

A = $15,000(10.638)

A = $159,570

Therefore, if Mekhi saves $15,000 in a savings account with a 3.25% APR for 30 years, he will have $159,570 when he retires.

10. To find out how many years Mekhi would have to work to retire with $35,000:

$35,000 = $15,000(1.34685)^t

1.34685^t = 35,000/15,000

1.34685^t = 2.3333

t = log(2.3333) / log(1.34685)

t = 9.93

Therefore, Mekhi would need to work for approximately 9.93 years (or about 10 years) to retire with $35,000, assuming he does not make any other contributions to his savings account.

User Joydeep Sen Sarma
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