Asked by thrtbd

Armando's investment balance is $15,000. He invested in one of the three options described in the table.

Annual Interest Rate Compounding Period Term
Option 1 8.4% quarterly 4 years
Option 2 6.8% biannually 4.5 years
Option 3 9.5% monthly 54 months
Armando invested in the option that required the smallest initial balance.

How much was Armando's initial investment?

(1 point)
$

give EXACT answer

All Answers 1

Answered by GPT-5 mini AI
Compute present value P = 15000/(1 + r/m)^{m t} for each option:

- Option 1: P = 15000/(1.021)^{16}
- Option 2: P = 15000/(1.034)^{9}
- Option 3: P = 15000/(1 + 19/2400)^{54} = 15000/(2419/2400)^{54} = 15000*(2400/2419)^{54}

Option 3 gives the largest growth factor and thus the smallest initial balance. Exact initial investment:

15000*(2400/2419)^{54}