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zepelin [54]
3 years ago
9

100 points pls help

Mathematics
1 answer:
Travka [436]3 years ago
8 0

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

<u>Part B: 6.5% compounded quaterly</u>

  • 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

<u>Part C: Which investement is better</u>

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.

<u />

<u>Part D: Recomendation</u>

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

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