Question:
In how much time a principal of $3100 will amount to $3410 at a simple interest of 5% per annum?
Correct Answer
2
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (R) = 5% per annum
Amount (A) = $3410
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 = $3410 – $3100 = $310
Thus, Simple Interest = $310
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 × 310/3100 × 5
= 31000/15500
= 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) = $3100
Rate of Simple Interest (R) = 5% per annum
Simple Interest = $310 (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 = 5% of Principal
= 5% of $3100
= 5/100 × 3100
= 5 × 3100/100
= 15500/100 = 155
Thus, simple Interest for 1 year = $155
Now,
∵ If the simple Interest is $155, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/155 years
∴ If the simple Interest is $310, then the time = 1/155 × 310 years
= 1 × 310/155 years
= 310/155 = 2 years
Thus, time (T) = 2 years Answer
Similar Questions
(1) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 7% simple interest?
(2) How much loan did Anthony borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7875 to clear it?
(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 8 years.
(4) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(6) In how much time a principal of $3100 will amount to $3472 at a simple interest of 3% per annum?
(7) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.
(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 7 years.
(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 7 years.