Question
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b) Calculate the compound interest earned on R15 000 deposited into a bank for 2 years @12\% p.a. interest.

Ask by Pritchard Bowers. in South Africa
Feb 24,2025

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Tutor-Verified Answer

Answer

The compound interest earned is R3,816.

Solution

To calculate the compound interest, use the formula for the amount A after n years:   A = P × (1 + r)ⁿ where:   P = initial principal (R15,000)   r = annual interest rate (12% or 0.12)   n = number of years (2) Step 1: Calculate the total amount after 2 years.   A = 15,000 × (1 + 0.12)²   A = 15,000 × (1.12)²   A = 15,000 × 1.2544   A = R18,816 Step 2: Determine the compound interest earned by subtracting the principal.   Compound Interest = A − P   Compound Interest = R18,816 − R15,000   Compound Interest = R3,816 So, the compound interest earned on the deposit over 2 years is R3,816.

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To calculate the compound interest earned, you can use the formula: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (R15,000), r is the annual interest rate (12% or 0.12), n is the number of times that interest is compounded per year (we'll assume annually, so n = 1), and t is the number of years the money is invested (2 years). Plugging in the numbers, A = 15,000(1 + 0.12/1)^(1*2) = 15,000(1 + 0.12)^2 = 15,000(1.12)^2 = 15,000(1.2544) ≈ R18,816. So, the compound interest earned is R18,816 - R15,000 = R3,816. It's amazing how compound interest can work in your favor! Just imagine it like planting a seed that grows into a big tree over time. The longer it stays planted, the bigger the tree (and your money) becomes! That's why starting early with investments can really pay off in the long run. Many people make the mistake of not considering the frequency of compounding, which can significantly affect the amount of interest earned. For example, if the interest is compounded quarterly or monthly instead of annually, you would end up with a higher amount due to interest being calculated on previously earned interest more frequently. Always check the compounding frequency when you calculate your interest!

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