Question

Veronique and Lily compare their investment accounts to see how much they will have in the accounts after seven years. They substitute their values shown below into the compound interest formula.

Compound Interest Accounts
Name
Principal
Interest Rate
Number of Years
Compounded
Veronique
$1,000
5%
7
Once a year
Lily
$1,800
9%
7
Once a year
A = P (1 + r) Superscript t

Which pair of equations would correctly calculate their compound interests?
Veronique: A = 1,000 (1 + 0.05) superscript 7, Lily: A = 1,800 (1 + 0.09) Superscript 7
Veronique: A = 1,000 (1 + 0.07) Superscript 5, Lily: A = 1,800 (1 + 0.07) Superscript 9
Veronique: A = 1,800 (1 + 0.05) Superscript 7, Lily: A = 1,000 (1 + 0.09) Superscript 7
Veronique: A = 1,000 (1 + 0.07) Superscript 5, Lily: A = 1,800 (1 + 0.07) Superscript 9

Answer 1

To calculate the future value of an investment using the compound interest formula \( A = P (1 + r)^t \), the values that need to be substituted for Veronique and Lily are as follows:

- **Veronique:**
- Principal (P) = $1,000
- Interest Rate (r) = 5% or 0.05
- Number of Years (t) = 7

Thus, Veronique's equation would be:
\[ A = 1,000 (1 + 0.05)^7 \]

- **Lily:**
- Principal (P) = $1,800
- Interest Rate (r) = 9% or 0.09
- Number of Years (t) = 7

Thus, Lily's equation would be:
\[ A = 1,800 (1 + 0.09)^7 \]

Therefore, the correct pair of equations is:
**Veronique: \( A = 1,000 (1 + 0.05)^7 \), Lily: \( A = 1,800 (1 + 0.09)^7 \)**