3.5. Diego took out a loan at $$ 6.2 \% $$ p.a. compound interest. Calculate the amount he borrowed if he repays the loan in four years with R 720000.

Question

UpStudy AI · Accepted Answer

To find the amount Diego borrowed, we can use the formula for compound interest, which is given by:

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

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

In this case:
- $$ A = 720000 $$
- $$ r = 6.2\% = 0.062 $$
- $$ n = 4 $$

We need to rearrange the formula to solve for $$ P $$:

$$
P = \frac{A}{(1 + r)^n}
$$

Now, we can substitute the known values into the formula to calculate $$ P $$.

Let's calculate $$ P $$ step by step.

1. Calculate $$ (1 + r) $$:
   $$
   1 + r = 1 + 0.062
   $$

2. Raise the result to the power of $$ n $$:
   $$
   (1 + r)^n = (1 + 0.062)^4
   $$

3. Finally, calculate $$ P $$:
   $$
   P = \frac{720000}{(1 + 0.062)^4}
   $$

Now, let's perform these calculations.
Calculate the value by following steps:
- step0: Calculate:
  $$1+0.062$$
- step1: Add the numbers:
  $$1.062$$
Calculate or simplify the expression $$ (1 + 0.062)^4 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(1+0.062\right)^{4}$$
- step1: Add the numbers:
  $$1.062^{4}$$
- step2: Convert the expressions:
  $$\left(\frac{531}{500}\right)^{4}$$
- step3: Use the properties of exponents:
  $$\frac{531^{4}}{500^{4}}$$
Calculate or simplify the expression $$ 720000 / 1.272032 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{720000}{1.272032}$$
- step1: Convert the expressions:
  $$\frac{720000}{\frac{39751}{31250}}$$
- step2: Multiply by the reciprocal:
  $$720000\times \frac{31250}{39751}$$
- step3: Multiply:
  $$\frac{720000\times 31250}{39751}$$
- step4: Multiply:
  $$\frac{22500000000}{39751}$$
Let's summarize the calculations step by step:

1. Calculate $$ 1 + r $$:
   $$
   1 + 0.062 = 1.062
   $$

2. Raise $$ 1.062 $$ to the power of $$ 4 $$:
   $$
   (1.062)^4 \approx 1.272032
   $$

3. Now, we can calculate $$ P $$:
   $$
   P = \frac{720000}{1.272032} \approx 566023.50
   $$

Thus, the amount Diego borrowed is approximately **R 566023.50**.
Diego borrowed approximately R 566,023.50.

3.5. Diego took out a loan at \( 6.2 \% \) p.a. compound interest. Calculate the amount he borrowed if he repays the loan in four years with R 720000.

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Arithmetic Questions