Question

assignment 3 - simple interest

1. match each variable with a value by placing the correct letter on each line.

variable\t\t\tvalue
a) principal\t\t_____ 280 days
b) interest\t\t_____ 1.95%
c) interest rate\t_____ $2000
d) term\t\t\t_____ $29.92

e) using the values above, calculate whether the interest earned is the correct amount.

f) what is the total value of this investment?

1. calculate the amount of simple interest earned in each of the situations.

a) principal = $1500\tinterest rate = 2.5%\tterm = 5 years

b) principal = $3245\tinterest rate = 7.5%\tterm = 3 years

c) principal = $500\tinterest rate = 11%\tterm = 9 years

Explanation:

Part 1 - Matching Variables

• Principal is the initial amount invested, so it matches \$2000.
• Interest is the earned amount, so it matches \$29.92.
• Interest rate is a percentage, so it matches 1.95%.
• Term is the time period, so it matches 280 days.

Step 1: Recall Simple Interest Formula

The formula for simple interest is \( I = P \times r \times t \), where:

• \( P = \$2000 \) (principal),
• \( r = 1.95\% = 0.0195 \) (rate),
• \( t = \frac{280}{365} \) (term in years, assuming a 365 - day year).

Step 2: Calculate Interest

Substitute values:
\( I = 2000 \times 0.0195 \times \frac{280}{365} \)
First, calculate \( 2000 \times 0.0195 = 39 \).
Then, \( 39 \times \frac{280}{365} \approx 39 \times 0.7671 \approx 29.92 \).

Step 1: Total Value Formula

Total value (A) is principal + interest: \( A = P + I \).

Step 2: Substitute Values

\( P = \$2000 \), \( I = \$29.92 \).
\( A = 2000 + 29.92 = 2029.92 \).

Answer:

a) principal → \$2000
b) interest → \$29.92
c) interest rate → 1.95%
d) term → 280 days

Part 1e - Verify Interest Amount