Question 2
If R35 000 accumulates to R48 320 at a continuous compounding rate of per year, determine the term
under consideration in years to two decimal places.

Question

Question 2 If R35 000 accumulates to R48 320 at a continuous compounding rate of $$ 8,6 \% $$ per year, determine the term under consideration in years to two decimal places.

UpStudy AI · Accepted Answer

To determine the term under consideration in years, we can use the formula for continuous compounding:

$$ A = P \times e^{r \times t} $$

where:
- $$ A $$ is the amount after the term,
- $$ P $$ is the principal amount (initial amount),
- $$ r $$ is the continuous compounding rate,
- $$ t $$ is the term in years.

Given:
- $$ A = 48,320 $$ (amount after the term),
- $$ P = 35,000 $$ (principal amount),
- $$ r = 8.6\% $$ (continuous compounding rate).

We need to solve for $$ t $$ (term in years).

Substitute the given values into the formula:

$$ 48,320 = 35,000 \times e^{0.086 \times t} $$

Now, we can solve for $$ t $$ using the formula:

$$ t = \frac{\ln\left(\frac{48,320}{35,000}\right)}{0.086} $$

Let's calculate the value of $$ t $$ using the formula.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\ln{\left(\frac{48320}{35000}\right)}}{0.086}$$
- step1: Reduce the fraction:
  $$\frac{\ln{\left(\frac{1208}{875}\right)}}{0.086}$$
- step2: Rewrite the expression:
  $$\frac{\ln{\left(\frac{1208}{875}\right)}}{\frac{43}{500}}$$
- step3: Multiply by the reciprocal:
  $$\ln{\left(\frac{1208}{875}\right)}\times \frac{500}{43}$$
- step4: Multiply the terms:
  $$\frac{\ln{\left(\frac{1208}{875}\right)}\times 500}{43}$$
- step5: Multiply the terms:
  $$\frac{500\ln{\left(\frac{1208}{875}\right)}}{43}$$
The term under consideration in years is approximately 3.75 years to two decimal places.
The term under consideration is approximately 3.75 years.

Question 2
If R35 000 accumulates to R48 320 at a continuous compounding rate of per year, determine the term
under consideration in years to two decimal places.

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Question 2 If R35 000 accumulates to R48 320 at a continuous compounding rate of per year, determine the term under consideration in years to two decimal places.

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Question 2
If R35 000 accumulates to R48 320 at a continuous compounding rate of per year, determine the term
under consideration in years to two decimal places.