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Activity #17

If the principal amount, rate, and time are given, find the interest and the total amount.

i. Rs. 900 for 3 years at [tex]$6\%$[/tex]
ii. Rs. 16000 for 3 years at [tex]$5\%$[/tex]
iii. Rs. 27000 for 4 years at [tex]$3\%$[/tex]
iv. Rs. 45000 for 2 years at [tex]$4\%$[/tex]
v. Rs. 35000 for 2 years at [tex]$7\%$[/tex]

Sagot :

GinnyAnswer
Sure, let's solve each of these step-by-step!

The formula to calculate simple interest is:
[tex]\[ \text{Interest} = \frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100} \][/tex]

And the amount after interest is added is:
[tex]\[ \text{Amount} = \text{Principal} + \text{Interest} \][/tex]

Let's break it down for each given principal amount, rate, and time:

### i. Rs. 900 for 3 years at 6%

1. Principal (P) = Rs. 900
2. Rate (R) = 6%
3. Time (T) = 3 years

Calculate the interest:
[tex]\[ \text{Interest} = \frac{900 \times 6 \times 3}{100} = 162 \][/tex]

Calculate the amount:
[tex]\[ \text{Amount} = 900 + 162 = 1062 \][/tex]

So, the interest is Rs. 162 and the amount is Rs. 1062.

### ii. Rs. 16000 for 3 years at 5%

1. Principal (P) = Rs. 16000
2. Rate (R) = 5%
3. Time (T) = 3 years

Calculate the interest:
[tex]\[ \text{Interest} = \frac{16000 \times 5 \times 3}{100} = 2400 \][/tex]

Calculate the amount:
[tex]\[ \text{Amount} = 16000 + 2400 = 18400 \][/tex]

So, the interest is Rs. 2400 and the amount is Rs. 18400.

### iii. Rs. 27000 for 4 years at 3%

1. Principal (P) = Rs. 27000
2. Rate (R) = 3%
3. Time (T) = 4 years

Calculate the interest:
[tex]\[ \text{Interest} = \frac{27000 \times 3 \times 4}{100} = 3240 \][/tex]

Calculate the amount:
[tex]\[ \text{Amount} = 27000 + 3240 = 30240 \][/tex]

So, the interest is Rs. 3240 and the amount is Rs. 30240.

### iv. Rs. 45000 for 2 years at 4%

1. Principal (P) = Rs. 45000
2. Rate (R) = 4%
3. Time (T) = 2 years

Calculate the interest:
[tex]\[ \text{Interest} = \frac{45000 \times 4 \times 2}{100} = 3600 \][/tex]

Calculate the amount:
[tex]\[ \text{Amount} = 45000 + 3600 = 48600 \][/tex]

So, the interest is Rs. 3600 and the amount is Rs. 48600.

### v. Rs. 35000 for 2 years at 7%

1. Principal (P) = Rs. 35000
2. Rate (R) = 7%
3. Time (T) = 2 years

Calculate the interest:
[tex]\[ \text{Interest} = \frac{35000 \times 7 \times 2}{100} = 4900 \][/tex]

Calculate the amount:
[tex]\[ \text{Amount} = 35000 + 4900 = 39900 \][/tex]

So, the interest is Rs. 4900 and the amount is Rs. 39900.

In summary:
1. Rs. 900 for 3 years at 6% results in an interest of Rs. 162 and an amount of Rs. 1062.
2. Rs. 16000 for 3 years at 5% results in an interest of Rs. 2400 and an amount of Rs. 18400.
3. Rs. 27000 for 4 years at 3% results in an interest of Rs. 3240 and an amount of Rs. 30240.
4. Rs. 45000 for 2 years at 4% results in an interest of Rs. 3600 and an amount of Rs. 48600.
5. Rs. 35000 for 2 years at 7% results in an interest of Rs. 4900 and an amount of Rs. 39900.
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