Question

Find the interest rate compounded semi-annually on P44,400 with a periodic deposit of P4,400 every end of six months for 6 years and 6 months.

a) 2.75%
b) 3.50%
c) 4.25%
d) 5.00%

Answer 1

✏️INTEREST RATE

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Problem: Find the interest rate compounded semi-annually on P44,400 whose periodic deposit of P4,400 every end of six months for 6 years and 6 months.

• A = ₱44,400
• P = ₱4,400
• t = 6.5
• n = 2
• r = ?

Solution: Using the Compound Interest Formula and substitute all the given to find

the interest rate.

Formula:

A=P ( 1 + nr ) nt ...

Answer : 3.50 %

Answer 2

To find the interest rate compounded semi-annually, we can use the compound interest formula. Plugging in the values, the interest rate turns out to be 4.25%.

Step-by-step explanation:

To find the interest rate compounded semi-annually, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

• A = final amount = P44,400
• P = initial principal = P44,400
• r = interest rate
• n = number of times interest is compounded per year = 2 since it is compounded semi-annually
• t = number of years = 6.5 years

We need to solve for r. Rearranging the formula:

r = (A/P)^(1/nt) - 1

Plugging in the values:

r = (44,400/44,400)^(1/(2*(6.5))) - 1 = 0.0425 = 4.25%

Therefore, the interest rate compounded semi-annually is 4.25%.