4.1 To calculate Mrs. May's annual income before she received the increase, we need to reverse the increase calculation.
Let's assume her annual income before the increase is X.
After receiving an increase of 6.5%, her new annual income becomes:
X + 6.5% of X = X + (0.065 * X) = 1.065 * X
Given that her new annual income is R 336,000, we can set up the equation:
1.065 * X = R 336,000
To find X, we divide both sides of the equation by 1.065:
X = R 336,000 / 1.065
X ≈ R 315,492.96
Therefore, Mrs. May's annual income before she received the increase was approximately R 315,492.96.
4.2 To calculate how much money will be paid out to her after the two-year period, we can calculate the compound interest for each year and add it to the initial investment.
The initial investment is the annual bonus she used, which is equal to her monthly salary without deductions. Since the problem does not provide the exact amount, we cannot calculate the exact payout. However, we can calculate the payout based on a general assumption.
Let's assume the annual bonus she used is X.
For the first year, the interest rate is 5.8%. Therefore, the investment after the first year is:
X + 5.8% of X = X + (0.058 * X) = 1.058 * X
For the second year, the interest rate is 6.5%. Therefore, the investment after the second year is:
1.058 * X + 6.5% of (1.058 * X) = 1.058 * X + (0.065 * 1.058 * X) = 1.058 * X + (0.06887 * X) = 1.12687 * X
The payout after the two-year period is the final investment, which is 1.12687 times the initial investment:
Payout = 1.12687 * X
Since the problem does not provide the exact value of X, we cannot calculate the exact payout amount. However, you can substitute the value of X (Mrs. May's annual bonus) into the equation to calculate the specific payout amount based on the given information.