Advertisements
Advertisements
प्रश्न
The compound interest payable annually on a certain sum for 2 years is Rs 40.80 and the simple interest is Rs 40. Find the sum and the rate percent.
Advertisements
उत्तर
Let sum be Rs. P and r % be the rate of interest.
We have t = 2 years, C.I. = Rs.40.80 and S.I. = Rs.40
Since, Simple interest
= `("P" xx "r" xx "t")/(100)`
⇒ 40 = `("P" xx "r" xx 2)/(100)`
⇒ Pr = `(4000)/(2)`
= 2000
Now,
C.I. = A - P
= `"P"(1 + "r"/100)^"t" - "P"`
= `"P"[(1 + "r"/100)]^"t" - 1]`
⇒ 40.80 = `"P"[(1 + "r"/100)^2 - 1]`
⇒ 40.80 = `"P"(1 + "r"^2/10000 + (2"r")/100 - 1)`
⇒ 40.80 = `"P"("r"^2/10000 + (2"r")/100)`
⇒ 40.80 = `"Pr"("r"/10000 + (2)/100)`
⇒ 40.80 = `2000(("r" + 200)/10000)`
⇒ 40.80 = `("r" + 200)/(5)`
⇒ r = 40.80 x 5 - 200
= 204 - 200
= 4
Hence, r = 4%
Now, Pr = 2000
⇒ P = `(2000)/"r"`
= `(2000)/(4)`
= 500.
Thus, sum is Rs.500 and rate of interest is 4%.
APPEARS IN
संबंधित प्रश्न
Calculate the amount and compound interest on Rs 62500 for `1 1/2` years at 8% per annum compounded half yearly.
Calculate the amount and compound interest on Rs 8000 for 1 year at 9% per annum compound half yearly. (You could use the year by year calculation using SI formula to verify)
Rachana borrowed a certain sum at the rate of 15% per annum. If she paid at the end of two years Rs 1290 as interest compounded annually, find the sum she borrowed.
The difference between the compound interest and simple interest on a certain sum for 2 years at 7.5% per annum is Rs 360. Find the sum.
The difference in simple interest and compound interest on a certain sum of money at \[6\frac{2}{3} %\] per annum for 3 years is Rs 46. Determine the sum.
The cost of a machine depreciated by Rs. 4,000 during the first year and by Rs. 3,600 during the second year. Calculate :
- The rate of depreciation.
- The original cost of the machine.
- Its cost at the end of the third year.
A man borrows Rs.10,000 at 10% compound interest compounded yearly. At the end of each year, he pays back 20% of the amount for that year. How much money is left unpaid just after the second year ?
On a certain sum of money, invested at the rate of 10 percent per annum compounded annually, the interest for the first year plus the interest for the third year is Rs. 2,652. Find the sum.
Calculate the compound interest on Rs. 5,000 in 2 years; if the rates of interest for successive years be 10% and 12% respectively.
Calculate the compound interest for the second year on Rs. 15000 invested for 5 years at 6% per annum.
A man invests Rs. 9600 at 10% per annum compound interest for 3 years. Calculate :
(i) the interest for the first year.
(ii) the amount at the end of the first year.
(iii) the interest for the second year.
(iv) the interest for the third year. the interest for the first year.
Calculate the difference between the compound interest and the simple interest on ₹ 8,000 in three years and at 10% per annum.
The difference between simple interest and compound interest compounded annually on a certain sum is Rs.448 for 2 years at 8 percent per annum. Find the sum.
The difference between C.I. payable annually and S.I. on Rs.50,000 for two years is Rs.125 at the same rate of interest per annum. Find the rate of interest.
The compound interest on ₹ 5000 at 12% p.a for 2 years, compounded annually is ___________
Depreciation value is calculated by the formula, `"P"(1 - "r"/100)^"n"`
If the present population of a city is P and it increases at the rate of r% p.a, then the population n years ago would be `"P"(1 + "r"/100)^"n"`
The time taken for ₹ 1000 to become ₹ 1331 at 20% p.a, compounded annually is 3 years
Find the compound interest for `2 1/2` years on ₹ 4000 at 10% p.a, if the interest is compounded yearly
A principal becomes ₹ 2028 in 2 years at 4% p.a compound interest. Find the principal
In how many years will ₹ 3375 become ₹ 4096 at `13 1/3` p.a if the interest is compounded half-yearly?
The compound interest on Rs 50,000 at 4% per annum for 2 years compounded annually is ______.
To calculate the growth of a bacteria if the rate of growth is known, the formula for calculation of amount in compound interest can be used.
Find the difference between Compound Interest and Simple Interest on Rs 45,000 at 12% per annum for 5 years.
