Question

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)
$

Answer 1

Compute the present value P = 15000 / (1 + r/n)^(n t) for each option.

Option 1: P = 15000 / (1 + 0.084/4)^(4·4) = 15000 / 1.021^16 ≈ $10,756.74
Option 2: P = 15000 / (1 + 0.068/2)^(2·4.5) = 15000 / 1.034^9 ≈ $11,096.30
Option 3: P = 15000 / (1 + 0.095/12)^(54) = 15000 / 1.0079167^54 ≈ $9,798.48

The smallest initial balance is from Option 3: approximately $9,798.48.