Question

100 points pls help

George is considering two different investment options. The first option offers 7.4% per year simple interest on the initial deposit. The second option offers a 6.5% interest rate but is compounded quarterly. He may not withdraw any of the money for three years after the initial deposit. Once the minimum 3 years is reached, he can choose to withdraw his money or continue to collect interest. Suppose that George opens one of each type of account and deposits $10,000 into each.

Answer 1

Answer:

• Part A: $12,220

• Part B: $12,134.08

• Part C: First option

• Parte C: Second option.

Explanation:

Part A: 7.4% simple interest

• r = 7.4% = 0.074
• P = $10,000
• t = 3 years

Formula: $A=P+Prt$

Calculations:

        $A= 10,000+ 10,000(7.4\%)(3)\\\\ A=\ 10,000+\ 10,000(0.074)(3)\\\\ A=\ 12,220$

Part B: 6.5% compounded quaterly

• r = 6.5% = 0.065

• n = 4

• P = $10,000

• t = 3 years

Formula:

         $A=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}$

Substitute and compute:

        $A=\ 10,000\bigg(1+\dfrac{0.065}{4}\bigg)^{(4\times3)}$

        $A=\ 12,134.08$

Part C: Which investement is better

Over the first three years the first option, 7.4% per year simple interest, is a better investment, because the value of its value is $12,220 - $12,134.0 = $85.94 greater than the second option.

Part D: Recomendation

If George is unsure how long he will keep the money in the account, I would recommend to use the second option, because the compounded interest will overcome the simple interest, since the year 5.  You can show that with a table:

Value of A in $:

Year         Simplet intertest                         Compound interest

1                10,000 + 10,000(0.074)(1)             10,000(1 + 0.0650/4)¹

                 10,740                                           10,666

2              10,000 + 10,000(0.074)(2)             10,000(1 + 0.065/4)²

                11,480                                              11,376

3             10,000 + 10,000(0.074)(3)               10,000(1 + 0.0650/4)³

              12,220                                               12,314

4             10,000 + 10,000(0.074)(4)               10,000(1 + 0.065/4)⁴

              12,960                                               12,942

5             10,000 + 10,000(0.074)(5)                10,000(1 + 0.065/4)⁵

              13,700                                                13,804