Math Problem Statement

Consider a single sum of money of 800,000/= deposited into a fixed deposit account earning 4% interest compounded annually. How much would have your deposit have grown by the end of 5 years?

Solution

To calculate the future value of a fixed deposit account with compounded interest, we can use the formula:

A=P(1+r)nA = P (1 + r)^n

where:

  • AA is the amount of money accumulated after n years, including interest.
  • PP is the principal amount (the initial sum of money).
  • rr is the annual interest rate (decimal).
  • nn is the number of years the money is invested or borrowed.

Given:

  • P=800,000P = 800,000
  • r=0.04r = 0.04 (4%)
  • n=5n = 5

Now, substituting the values into the formula:

A=800,000×(1+0.04)5A = 800,000 \times (1 + 0.04)^5 A=800,000×(1.04)5A = 800,000 \times (1.04)^5 A=800,000×1.216652902A = 800,000 \times 1.216652902 A973,322.32A \approx 973,322.32

Therefore, the deposit would have grown to approximately 973,322.32 after 5 years.

To find out how much the deposit has grown, we subtract the initial deposit from the future value:

Growth=AP=973,322.32800,000=173,322.32\text{Growth} = A - P = 973,322.32 - 800,000 = 173,322.32

Thus, the deposit would have grown by approximately 173,322.32 over 5 years.

Would you like more details on this calculation, or do you have any questions? Here are some related questions you might consider:

  1. What would the total amount be after 10 years at the same interest rate?
  2. How does changing the interest rate to 5% affect the total amount after 5 years?
  3. What is the difference between simple interest and compound interest?
  4. How would the growth change if the interest were compounded semi-annually instead of annually?
  5. What are some common types of fixed deposit accounts available?

Tip: Always verify the interest compounding frequency as it significantly impacts the growth of your investment.

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Math Problem Analysis

Mathematical Concepts

Compound Interest
Exponential Growth

Formulas

Compound Interest Formula: A = P(1 + r)^n

Theorems

Exponential Growth with Compounded Interest

Suitable Grade Level

Grades 10-12