No.3 At what annual rate of compound interest will R2000 grow to R2721 after 4 years?

Question

ScanSolve AI Tutor · Accepted Answer

Step 1: Write down the formula for compound interest. A = P(1 + r)ⁿ Where: A = Final amount; P = Principal amount; r = Annual interest rate (as a decimal); n = Number of years Step 2: Substitute the given values into the formula. A = R2721; P = R2000; n = 4 years; 2721 = 2000(1 + r)⁴ Step 3: Isolate the term (1 + r)⁴. 2721 / 2000 = (1 + r)⁴; 1.3605 = (1 + r)⁴ Step 4: Take the 4th root of both sides to solve for (1 + r). ⁴√(1.3605) = 1 + r; 1.0800 = 1 + r (rounded to 4 decimal places) Step 5: Solve for r. r = 1.0800 − 1; r = 0.0800 Step 6: Convert the decimal rate to a percentage. Rate = 0.0800 × 100%; Rate = 8%

No.3 At what annual rate of compound interest will R2000 grow to R2721 after 4 years?

Step-by-step solution

Write down the formula for compound interest.

Substitute the given values into the formula.

Isolate the term (1 + r)⁴.

Take the 4th root of both sides to solve for (1 + r).

Solve for r.

Convert the decimal rate to a percentage.

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