Question

Mrs. Guevara plans to invest Php 20 000. Her goal was to eam Php 10000 interest. She considered investing on a bank which offers 5.6% interest compounded annually. For how long does she have to leave her money in the bank in order to earn the interest she aims to have?

Answer 1

Mrs. Guevara needs to keep her Php 20,000 invested for approximately 12 years at a 5.6% annual compound interest rate to earn Php 10,000 in interest.

Step-by-step explanation:

Mrs. Guevara's goal is to earn Php 10,000 in interest from an initial investment of Php 20,000. The bank offers an annual compound interest rate of 5.6%. We can calculate the time needed to reach her investment goal using the formula for compound interest:

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

Where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for in years.

Here, P is Php 20,000, r is 0.056 (5.6%), n is 1 (since the interest is compounded annually), and we want to find t when A is equal to the initial principal plus the desired interest: Php 20,000 + Php 10,000 = Php 30,000.

We can rearrange the formula to solve for t:

t = ln(A/P) / (n * ln(1 + r/n))

Substituting the values we have:

t = ln(30,000/20,000) / (1 * ln(1 + 0.056/1))

t ≈ 11.9 years

Mrs. Guevara will need to leave her money in the bank for approximately 12 years to earn the Php 10,000 in interest she desires.