Question

Arnold and Azura want to save ₱500,000 in 5.5years to renovate their rest house. If the Bank of Amber is paying 8% interest compounded quarterly, how much must they deposit now in order to have the money for the project?

Answer 1

They must deposit ₱196,386.4886 now.

Step-by-step explanation

Amount = ₱500,000

n = 5.5 x 4 = 22

Rate, r = 8/4 = 2%

Principal, P = ?

The Compound Interest, I, is given by the formula:

`I=P(1+(r)/(100))^n`

Also,

`I=A-P`

Equating the two equations above, gives

`A-P=P(1+(r)/(100))^n`
`\begin{gathered} 500,000-P=P(1+(2)/(100))^(22) \\ 500,000-P=P(1.02)^(22) \\ 500,000-P=P(1.546) \\ 500,000=P+1.546P \\ 500,000=2.546P \\ P=(500,000)/(2.546) \\ P=196,386.4886 \end{gathered}`

Therefore, they must deposit ₱196,386.4886 now in order to

have the money for the project.​