We will discuss here about the principle of compound interest in the combination of uniform rate of growth and depreciation.

If a quantity P grows at the rate of r\(_{1}\)% in the first year, depreciates at the rate of r\(_{2}\)% in the second year and grows at the rate of r\(_{3}\)% in the third year then the quantity becomes Q after 3 years, where

Take \(\frac{r}{100}\) with positive sign for each growth or appreciation of r% and \(\frac{r}{100}\) with negative sign for each depreciation of r%.

Solved examples on the principle of compound interest in the uniform rate of depreciation:

**1. **The present population of a town is 75,000. The population increases by 10 percent is the first year and decreases by 10% in the second year. Find the population after 2 years.

**Solution:**

Here, initial population P = 75,000, population increase for the first year =
r\(_{1}\)% = 10% and decrease for the second year = r\(_{2}\)% = 10%.

Population after 2 years:

Q = P(1 + \(\frac{r_{1}}{100}\))(1 - \(\frac{r_{2}}{100}\))

⟹ Q = Present population(1 + \(\frac{r_{1}}{100}\))(1 - \(\frac{r_{2}}{100}\))

⟹ Q = 75,000(1 + \(\frac{10}{100}\))(1 - \(\frac{10}{100}\))

⟹ Q = 75,000(1 + \(\frac{1}{10}\))(1 - \(\frac{1}{10}\))

⟹ Q = 75,000(\(\frac{11}{10}\))(\(\frac{9}{10}\))

⟹ Q = 74,250

Therefore, the population after 2 years = 74,250

**2.** A man starts a business with a capital of $1000000. He
incurs a loss of 4% during the first year. But he makes a profit of 5% during
the second year on his remaining investment. Finally, he makes a profit of 10%
on his new capital during the third year. Find his total profit at the end of
three years.

**Solution:**

Here, initial capital P = 1000000, loss for the first year = r\(_{1}\)% = 4%, gain for the second year = r\(_{2}\)% = 5% and gain for the third year = r\(_{3}\)% = 10%

Q = P(1 - \(\frac{r_{1}}{100}\))(1 + \(\frac{r_{2}}{100}\))(1 + \(\frac{r_{3}}{100}\))

⟹ Q = $1000000(1 - \(\frac{4}{100}\))(1 + \(\frac{5}{100}\))(1 + \(\frac{10}{100}\))

Therefore, Q = $1000000 × \(\frac{24}{25}\) × \(\frac{21}{20}\) × \(\frac{11}{10}\)

⟹ Q = $200 × 24 × 21 × 11

⟹ Q = $1108800

Therefore, profit at the end of three years = $1108800 - $1000000

= $108800

**● Compound Interest**

**Compound Interest with Growing Principal**

**Compound Interest with Periodic Deductions**

**Compound Interest by Using Formula**

**Compound Interest when Interest is Compounded Yearly**

**Compound Interest when Interest is Compounded Half-Yearly**

**Compound Interest when Interest is Compounded Quarterly**

**Variable Rate of Compound Interest**

**Difference of Compound Interest and Simple Interest**

**Practice Test on Compound Interest**

**● Compound Interest - Worksheet**

**Worksheet on Compound Interest**

**Worksheet on Compound Interest when Interest is Compounded Half-Yearly**

**Worksheet on Compound Interest with Growing Principal**

**Worksheet on Compound Interest with Periodic Deductions**

**Worksheet on Variable Rate of Compound Interest**

**8th Grade Math Practice****From Uniform Rate of Growth and Depreciation to HOME PAGE**

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