Question:
In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?
Correct Answer
2
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (R) = 4% per annum
Amount (A) = $3294
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are givenFormual to Calculate Simple Interest when Principal and Amount are given
We know that, Amount (A) = Principal (P) + Simple Interest (SI)
⇒ Simple Interest (SI) = Amount – Principal
⇒ SI = $3294 – $3050 = $244
Thus, Simple Interest = $244
Calculation of the Time using forumula when Amount, Simple Interest and Principal are known
Formula to find the Time (T)
Time (T) = 100 × Simple Interest/Principal × Rate of Interest
⇒ T = 100 × SI/P × R
Thus, Time (T) = 100 × 244/3050 × 4
= 24400/12200
= 2 years (using formula)
Thus, Time (T) = 2 years (from time taken before calculation)Answer
Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known
Here, we have
Principal (P) = $3050
Rate of Simple Interest (R) = 4% per annum
Simple Interest = $244 (As calculated above by subtracting Principal from the Amount given)
We know that, interest is calculated on the basis of the Principal.
This means Simple Interest for 1 year = Rate of simple interest × Principal
Thus, Simple Interest for 1 year = 4% of Principal
= 4% of $3050
= 4/100 × 3050
= 4 × 3050/100
= 12200/100 = 122
Thus, simple Interest for 1 year = $122
Now,
∵ If the simple Interest is $122, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/122 years
∴ If the simple Interest is $244, then the time = 1/122 × 244 years
= 1 × 244/122 years
= 244/122 = 2 years
Thus, time (T) = 2 years Answer
Similar Questions
(1) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 7 years.
(2) James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 5% simple interest.
(4) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(5) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 4 years.
(7) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 5% simple interest?
(8) How much loan did Carol borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8107.5 to clear it?
(9) If William borrowed $3500 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.