Question

Aaron Abbott invested ₱100,000 at 12% interest, compounded semi-annually, for 3 years. Calculate the compound amount and the compound interest of Aaron’s investment.

Answer 1

The compound amount is ₱141,851.91

The compound interest is ₱41,851.91

Explanations:

The formula for calculating the compound interest is expressed according to the formula:

`\text{ A = P(1 + }(r)/(n)\text{)}^(nt)`

P is the principal (money invested)

r is the rate (in decimal)

t is the time (in years)

n is the compounding time

Given the following parameters

P = ₱100,000

r = 12% = 0.12

t = 3 years

n = 2(semi-annually)

Substitute the given parameters into the formula

`\begin{gathered} \text{ A = 100,000}(1+(0.12)/(2))^(2(3))^{} \\ \text{ A = 100,000(1+}0.06\text{)}^6 \\ \text{ A = 100,000(1.06)}^6 \\ \text{ A = 100,000(}1.4185\text{)} \\ \text{ A = }₱141,851.91 \end{gathered}`

This shows that the compound amount is ₱141,851.91

Get the compound interest:

Compound interest = Compound amount - Principal

Compound interest = 141,851.91 - 100,000

Compound interest = ₱41,851.91

Hence the compound interest of Aaron’s investment is ₱41,851.91