1. Calculate the final amount if you invest? a) RZ swo ai $$ 8 \% $$ compounded interest p.a for 2 years b) 275000 at $$ 7.5 \% $$ p.a compounded annually for 3 years

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UpStudy AI · Accepted Answer

Calculate the value by following steps:
- step0: Calculate:
  $$275000\left(1+0.08\right)^{2}$$
- step1: Add the numbers:
  $$275000\times 1.08^{2}$$
- step2: Convert the expressions:
  $$275000\left(\frac{27}{25}\right)^{2}$$
- step3: Evaluate the power:
  $$275000\times \frac{729}{625}$$
- step4: Multiply:
  $$320760$$
Calculate or simplify the expression $$ 275000*(1+0.075)^3 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$275000\left(1+0.075\right)^{3}$$
- step1: Add the numbers:
  $$275000\times 1.075^{3}$$
- step2: Convert the expressions:
  $$275000\left(\frac{43}{40}\right)^{3}$$
- step3: Simplify:
  $$275000\times \frac{43^{3}}{40^{3}}$$
- step4: Evaluate the power:
  $$275000\times \frac{43^{3}}{64000}$$
- step5: Reduce the numbers:
  $$275\times \frac{43^{3}}{64}$$
- step6: Multiply:
  $$\frac{275\times 43^{3}}{64}$$
Let's calculate the final amounts for both investments step by step.

### a) Investment of RZ swo ai at $$ 8\% $$ compounded interest p.a for 2 years

The formula for compound interest is given by:

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

Where:
- $$ A $$ = the amount of money accumulated after n years, including interest.
- $$ P $$ = the principal amount (the initial amount of money).
- $$ r $$ = the annual interest rate (decimal).
- $$ n $$ = the number of years the money is invested or borrowed.

For this investment:
- $$ P = RZ $$ (we'll assume a principal amount of 1 for calculation purposes since the exact amount isn't provided)
- $$ r = 0.08 $$
- $$ n = 2 $$

Calculating:

$$
A = 1(1 + 0.08)^2 = 1(1.08)^2 = 1 \times 1.1664 = 1.1664
$$

If we assume $$ P = 1 $$ RZ, the final amount after 2 years would be approximately $$ 1.1664 $$ RZ.

### b) Investment of 275000 at $$ 7.5\% $$ p.a compounded annually for 3 years

Using the same formula:

For this investment:
- $$ P = 275000 $$
- $$ r = 0.075 $$
- $$ n = 3 $$

Calculating:

$$
A = 275000(1 + 0.075)^3 = 275000(1.075)^3
$$

The calculated final amount is approximately $$ 341631.64 $$.

### Summary of Results:
- a) Final amount for RZ swo ai at $$ 8\% $$ for 2 years: $$ 1.1664 $$ RZ (assuming $$ P = 1 $$)
- b) Final amount for 275000 at $$ 7.5\% $$ for 3 years: $$ 341631.64 $$
The final amounts are: - a) Approximately 1.1664 RZ after 2 years at 8% interest. - b) 341,631.64 after 3 years at 7.5% interest.

1. Calculate the final amount if you invest? a) RZ swo ai \( 8 \% \) compounded interest p.a for 2 years b) 275000 at \( 7.5 \% \) p.a compounded annually for 3 years

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