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:
Calculations:
<u>Part B: 6.5% compounded quaterly</u>
- r = 6.5% = 0.065
- n = 4
- P = $10,000
- t = 3 years
Formula:
Substitute and compute:
<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