Find the amount that $5,000.00 becomes if saved for 2 years at 6% per annum compound interest.
Answer (2)
After saving $5,000.00 for 2 years at a 6% annual compound interest rate, the total amount becomes $5,618.00. This amount is calculated using the compound interest formula which accounts for the effect of interest compounding over time. Understanding compound interest is essential for effective money management.
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Identify the principal amount, interest rate, and time period.
Apply the compound interest formula: A = P ( 1 + r ) n .
Substitute the given values into the formula: A = 5000 ( 1 + 0.06 ) 2 .
Calculate the final amount: A = #5 , 618.00 .
Explanation
Understanding the Problem We are given a principal amount of #5,000.00 that is saved for 2 years at an interest rate of 6% per annum, compounded annually. We need to find the final amount after 2 years.
Stating the Formula The formula for compound interest is given by: A = P ( 1 + r ) n where:
A is the amount after n years
P is the principal amount
r is the interest rate per annum
n is the number of years
Substituting the Values We are given:
P = #5 , 000.00
r = 6% = 0.06
n = 2 years Substituting these values into the formula, we get: A = 5000 ( 1 + 0.06 ) 2
Calculating the Final Amount Now, we calculate the value of A: A = 5000 ( 1.06 ) 2 A = 5000 × 1.1236 A = 5618
Final Answer Therefore, the amount after 2 years is #5,618.00
Examples
Compound interest is a powerful tool for growing wealth over time. For example, if you invest money in a retirement account that earns compound interest, your money will grow faster than if it only earned simple interest. Understanding compound interest can help you make informed decisions about saving and investing. For instance, knowing how compound interest works can motivate you to start saving early, as the earlier you start, the more time your money has to grow. Also, it helps in understanding the impact of interest rates on loans, mortgages, and other financial products.
