Question:
In how much time a principal of $3100 will amount to $3596 at a simple interest of 4% per annum?
Correct Answer
4
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (R) = 4% per annum
Amount (A) = $3596
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 = $3596 – $3100 = $496
Thus, Simple Interest = $496
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 × 496/3100 × 4
= 49600/12400
= 4 years (using formula)
Thus, Time (T) = 4 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) = $3100
Rate of Simple Interest (R) = 4% per annum
Simple Interest = $496 (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 $3100
= 4/100 × 3100
= 4 × 3100/100
= 12400/100 = 124
Thus, simple Interest for 1 year = $124
Now,
∵ If the simple Interest is $124, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/124 years
∴ If the simple Interest is $496, then the time = 1/124 × 496 years
= 1 × 496/124 years
= 496/124 = 4 years
Thus, time (T) = 4 years Answer
Similar Questions
(1) If Richard borrowed $3600 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(2) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 3 years.
(4) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 5% simple interest?
(5) In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?
(6) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 4% simple interest?
(7) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 4 years.
(8) How much loan did Betty borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7812.5 to clear it?
(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 3 years.
(10) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.