Question

Ben needs to have Php 20,000 after two years. Assuming that he will only deposit once, with a 5% interest compounded annually, how much will you deposit today?

A. Php 19,048.26
B. Php 19,200.00
C. Php 20,800.00
D. Php 20,858.90

Answer 1

To have Php 20,000 after two years with a 5% interest compounded annually, Ben should deposit approximately Php 18,140.57 today.

Step-by-step explanation:

To find the amount to deposit today, we can use the formula for compound interest:

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

Where:

• A is the future value (Php 20,000)
• P is the principal (the amount to be deposited today)
• r is the annual interest rate (5% or 0.05)
• n is the number of times interest is compounded per year (1, since it's compounded annually)
• t is the number of years (2)

Substituting the values into the formula, we get:

20,000 = P(1 + 0.05/1)^(1*2)

Simplifying, we have:

20,000 = P(1.05)^2

20,000 = P(1.1025)

Dividing both sides by 1.1025, we find that the amount to be deposited today is approximately Php 18,140.57