Question

General MathematicsProblem:How much should you set aside and invest in a fund earning 10% compounded quarterly if you want to accumulate ₱200,000 in 3 years and 6 months?

Answer 1

₱ 141545.4

Explanation:

We need to find the amount of money that must be invested to accumulate 200,000 in 3 years and 6 months. We use the following formula to calculate the principal amount P.

Since, the investment is made for 3 years and 6 months (3.5 years) therefore the formula for the compound interest compounded quarterly is:

`A=P\mleft(1+((r)/(4))/(100)\mright)^(4t)`

Replacing:

A = 200000

r = 10%

t = 3.5 years

`\begin{gathered} 200000=P\mleft(1+((10)/(4))/(100)\mright)^{^(4\cdot3.5)} \\ P=\frac{200000}{\mleft(1+(2.5)/(100)\mright)^{^(4\cdot3.5)}} \\ P=141545.4 \end{gathered}`

Hence, the amount of money to invest is ₱ 141545.4