Question:
In how much time a principal of $3100 will amount to $3565 at a simple interest of 3% per annum?
Correct Answer
5
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (R) = 3% per annum
Amount (A) = $3565
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 = $3565 – $3100 = $465
Thus, Simple Interest = $465
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 × 465/3100 × 3
= 46500/9300
= 5 years (using formula)
Thus, Time (T) = 5 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) = 3% per annum
Simple Interest = $465 (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 = 3% of Principal
= 3% of $3100
= 3/100 × 3100
= 3 × 3100/100
= 9300/100 = 93
Thus, simple Interest for 1 year = $93
Now,
∵ If the simple Interest is $93, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/93 years
∴ If the simple Interest is $465, then the time = 1/93 × 465 years
= 1 × 465/93 years
= 465/93 = 5 years
Thus, time (T) = 5 years Answer
Similar Questions
(1) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 7 years.
(2) If Joshua paid $5488 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) If Emily paid $5510 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 4 years.
(6) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 5% simple interest?
(7) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 8 years.
(9) If Sandra paid $5162 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) How much loan did George borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9125 to clear it?