Answer:
Explanation:
Part A: 7.4% simple interest
- r = 7.4% = 0.074
- P = $10,000
- t = 3 years
Formula: ![A=P+Prt](https://tex.z-dn.net/?f=A%3DP%2BPrt)
Calculations:
![A=$10,000+$10,000(7.4\%)(3)\\\\ A=\$10,000+\$10,000(0.074)(3)\\\\ A=\$12,220](https://tex.z-dn.net/?f=A%3D%2410%2C000%2B%2410%2C000%287.4%5C%25%29%283%29%5C%5C%5C%5C%20%20A%3D%5C%2410%2C000%2B%5C%2410%2C000%280.074%29%283%29%5C%5C%5C%5C%20%20A%3D%5C%2412%2C220)
<u>Part B: 6.5% compounded quaterly</u>
Formula:
![A=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}](https://tex.z-dn.net/?f=A%3DP%5Cbigg%281%2B%5Cdfrac%7Br%7D%7Bn%7D%5Cbigg%29%5E%7Bnt%7D)
Substitute and compute:
![A=\$10,000\bigg(1+\dfrac{0.065}{4}\bigg)^{(4\times3)}](https://tex.z-dn.net/?f=A%3D%5C%2410%2C000%5Cbigg%281%2B%5Cdfrac%7B0.065%7D%7B4%7D%5Cbigg%29%5E%7B%284%5Ctimes3%29%7D)
![A=\$12,134.08](https://tex.z-dn.net/?f=A%3D%5C%2412%2C134.08)
<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.
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<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