find out the time when a principal rs 700 gives a interest rs 98 at 7%
help pls explain
Answers
Answer:
Step-by-step explanation:
Simple interest = 27250 – 25000 = 2250
Time = 3 years.
SI = PTR / 100 → R = SI * 100 / PT
R = 2250 * 100 / 25000 * 3 → R = 3%.
Problem 2. Find the present worth of Rs. 78000 due in 4 years at 5% interest per year.
Solution:
Amount with interest after 4 years = Rs. 78000
Therefore, simple interest = 78000 – Principal.
Let the principal amount be p.
78000 – p = p*4*5/100 → p=13000
Principal = 78000 – 13000 = Rs. 65000
Problem 3. A certain principal amounts to Rs. 15000 in 2.5 years and to Rs. 16500 in 4 years at the same rate of interest. Find the rate of interest.
Solution:
Amount becomes 15000 in 2.5 years and 16500 in 4 years.
Simple interest for (4-2.5) years = 16500 – 15000
Therefore, SI for 1.5 years = Rs. 1500.
SI for 2.5 years = 1500/1.5 * 2.5 = 2500
Principal amount = 15000 – 2500 = Rs. 12500.
Rate of Interest = 2500 * 100 / 12500 * 2.5 → R = 8%.
Problem 4. Find the compound interest on Rs. 3000 at 5% for 2 years, compounded annually.
Solution:
Amount with CI = 3000 (1+ 5/100)2 = Rs. 3307.5
Therefore, CI = 3307.5 – 3000 = Rs. 307.5
Problem 5. Find the compound interest on Rs. 10000 at 12% rate of interest for 1 year, compounded half-yearly.
Solution:
Amount with CI = 10000 [1+ (12/2 * 100)]2 = Rs. 11236
Therefore, CI = 11236 – 10000 = Rs. 1236
Problem 6. The difference between SI and CI compounded annually on a certain sum of money for 2 years at 8% per annum is Rs. 12.80. Find the principal.
Solution:
Let the principal amount be x.
SI = x * 2 * 8 / 100 = 4x/25
CI = x[1+ 8/100]2 – x → 104x/625
Therefore, 104x/625 – 4x/25 = 12.80
Solving which gives x, Principal = Rs. 2000.
Problem 7. Find the simple interest on Rs. 5000 at a certain rate if the compound interest on the same amount for 2 years is Rs. 253.125.
Solution:
Let the rate of interest be r.
5000[1+ r/100]2 = 5000+253.125
→ [1+r/100]2 = 5253.125/5000
Solving which gives
[1+ r/100]2 = 1681/1600
→ 1+r/100 = 41/40
→ r = 2.5
Therefore, SI = 5000* 2 * 2.5/ 100 = Rs. 250.
Problem 8. A certain amount becomes Rs. 5760 in 2 years and Rs. 6912 in 3 years. What is the principal amount and the rate of interest?
Solution:Simple interest = 27250 – 25000 = 2250
Time = 3 years.
SI = PTR / 100 → R = SI * 100 / PT
R = 2250 * 100 / 25000 * 3 → R = 3%.
Problem 2. Find the present worth of Rs. 78000 due in 4 years at 5% interest per year.
Solution:
Amount with interest after 4 years = Rs. 78000
Therefore, simple interest = 78000 – Principal.
Let the principal amount be p.
78000 – p = p*4*5/100 → p=13000
Principal = 78000 – 13000 = Rs. 65000
Problem 3. A certain principal amounts to Rs. 15000 in 2.5 years and to Rs. 16500 in 4 years at the same rate of interest. Find the rate of interest.
Solution:
Amount becomes 15000 in 2.5 years and 16500 in 4 years.
Simple interest for (4-2.5) years = 16500 – 15000
Therefore, SI for 1.5 years = Rs. 1500.
SI for 2.5 years = 1500/1.5 * 2.5 = 2500
Principal amount = 15000 – 2500 = Rs. 12500.
Rate of Interest = 2500 * 100 / 12500 * 2.5 → R = 8%.
Problem 4. Find the compound interest on Rs. 3000 at 5% for 2 years, compounded annually.
Solution:
Amount with CI = 3000 (1+ 5/100)2 = Rs. 3307.5
Therefore, CI = 3307.5 – 3000 = Rs. 307.5
Problem 5. Find the compound interest on Rs. 10000 at 12% rate of interest for 1 year, compounded half-yearly.
Solution:
Amount with CI = 10000 [1+ (12/2 * 100)]2 = Rs. 11236
Therefore, CI = 11236 – 10000 = Rs. 1236
Problem 6. The difference between SI and CI compounded annually on a certain sum of money for 2 years at 8% per annum is Rs. 12.80. Find the principal.
Solution:
Let the principal amount be x.
SI = x * 2 * 8 / 100 = 4x/25
CI = x[1+ 8/100]2 – x → 104x/625
Therefore, 104x/625 – 4x/25 = 12.80
Solving which gives x, Principal = Rs. 2000.
Problem 7. Find the simple interest on Rs. 5000 at a certain rate if the compound interest on the same amount for 2 years is Rs. 253.125.
Solution:
Let the rate of interest be r.
5000[1+ r/100]2 = 5000+253.125
→ [1+r/100]2 = 5253.125/5000
Solving which gives
[1+ r/100]2 = 1681/1600
→ 1+r/100 = 41/40
→ r = 2.5
Therefore, SI = 5000* 2 * 2.5/ 100 = Rs. 250.
Problem 8. A certain amount becomes Rs. 5760 in 2 years and Rs. 6912 in 3 years. What is the principal amount and the rate of interest?