Question

assessment 1

1. find the simple interest and maturity value if ₱155 000 pesos is invested in a bank at an interest rate of 6% for a) 5 years and b) 9 months.
2. suppose you save ₱ 12 500.00 of your salary and deposit it into an account that earns simple interest. after 4 years, the balance is ₱15 000. what is the annual interest rate?
3. if ₱100 000 is invested at 6% simple interest, how long will it take to grow to ₱112 000?
4. how much is the principal amount or the present value borrowed if maturity value is ₱96 500 at 5% simple interest for 5 years?
5. jane borrowed a money from her friend and agreed to pay the simple interest of 5, 400 pesos at 12% simple interest for 6 months. how much is face value or the principal amount that she borrowed?

Explanation:

Problem 1

a) 5 years

Step 1: Recall simple interest formula

The formula for simple interest \( I \) is \( I = P \times r \times t \), where \( P \) is the principal amount, \( r \) is the annual interest rate (in decimal), and \( t \) is the time in years. The maturity value \( A \) is \( A = P + I \).
First, convert the interest rate to decimal: \( r = 6\% = 0.06 \), \( P = 155000 \), \( t = 5 \).

Step 2: Calculate simple interest

\( I = 155000 \times 0.06 \times 5 \)
\( I = 155000 \times 0.3 \)
\( I = 46500 \)

Step 3: Calculate maturity value

\( A = P + I = 155000 + 46500 = 201500 \)

b) 9 months

Step 1: Convert time to years

Since 1 year = 12 months, \( t = \frac{9}{12} = 0.75 \) years.

Step 2: Calculate simple interest

\( I = 155000 \times 0.06 \times 0.75 \)
\( I = 155000 \times 0.045 \)
\( I = 6975 \)

Step 3: Calculate maturity value

\( A = 155000 + 6975 = 161975 \)

Step 1: Recall simple interest formula for balance

The balance \( A = P + I \), and \( I = P \times r \times t \), so \( A = P(1 + rt) \). We know \( A = 15000 \), \( P = 12500 \), \( t = 4 \). We need to find \( r \).

Step 2: Rearrange formula to solve for \( r \)

From \( A = P(1 + rt) \), we get \( 1 + rt = \frac{A}{P} \), then \( rt = \frac{A}{P} - 1 \), and \( r = \frac{\frac{A}{P} - 1}{t} \)

Step 3: Substitute values

\( \frac{A}{P} = \frac{15000}{12500} = 1.2 \)
\( rt = 1.2 - 1 = 0.2 \)
\( r = \frac{0.2}{4} = 0.05 \) or \( 5\% \)

Step 1: Recall simple interest formula for amount

\( A = P + I = P(1 + rt) \). We know \( A = 112000 \), \( P = 100000 \), \( r = 6\% = 0.06 \). We need to find \( t \).

Step 2: Rearrange formula to solve for \( t \)

\( 1 + rt = \frac{A}{P} \)
\( rt = \frac{A}{P} - 1 \)
\( t = \frac{\frac{A}{P} - 1}{r} \)

Step 3: Substitute values

\( \frac{A}{P} = \frac{112000}{100000} = 1.12 \)
\( rt = 1.12 - 1 = 0.12 \)
\( t = \frac{0.12}{0.06} = 2 \) years

Answer:

a) Simple Interest: ₱46,500; Maturity Value: ₱201,500
b) Simple Interest: ₱6,975; Maturity Value: ₱161,975

Problem 2