Question

Duane and Thad plan on retiring 27 years from today and plan to have the same amount saved at that time. In preparation for this, Duane is depositing $15,000 today at an annual interest rate of 5.2 percent. How will Thad's deposit amount vary from Duane's if Thad also makes a deposit today but earns an annual interest rate of 6.2 percent?

Answer 1

Answer:

Thad deposited an amount of $11,241.58 about 27 years ago,

Step-by-step explanation:

About Duane:

The amount deposited by Duane = $15,000

Time interval = 27 years

Rate = 5.2%

Now, SIMPLE INTEREST  =  $\frac{P \times R \times T}{100}$

$\implies SI = \frac{15,000 \times 27 \times 5.2}{100} = 21,060$

So, the SI on 15,000 after 27 years = $21,060

Now, AMOUNT = PRINCIPAL + SI

                          = 15,000 + 21,060 = $36,060

Hence, after 27 years, Duane's amount is equivalent to $36,060

Now, About Thad:

Let us assume amount deposited  = P

Rate = 6.2%

Time = 27 y

Now, $SI = \frac{P \times 27 \times 6.2}{100} = 1.674 P$

So, the SI on 15,000 after 27 years = $1.674 P

Now, AMOUNT = PRINCIPAL + SI

        $36,060  = P +  1.674 P

      or, 2.624 P =  $36,060

⇒ P = 30,060/2.624 = 11,241.58

Hence, Thad deposited an amount of $11,241.58 about 27 years ago,