Question:
In how much time a principal of $3100 will amount to $3348 at a simple interest of 2% per annum?
Correct Answer
4
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (R) = 2% per annum
Amount (A) = $3348
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 = $3348 – $3100 = $248
Thus, Simple Interest = $248
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 × 248/3100 × 2
= 24800/6200
= 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) = 2% per annum
Simple Interest = $248 (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 = 2% of Principal
= 2% of $3100
= 2/100 × 3100
= 2 × 3100/100
= 6200/100 = 62
Thus, simple Interest for 1 year = $62
Now,
∵ If the simple Interest is $62, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/62 years
∴ If the simple Interest is $248, then the time = 1/62 × 248 years
= 1 × 248/62 years
= 248/62 = 4 years
Thus, time (T) = 4 years Answer
Similar Questions
(1) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.
(2) If Donald paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
(4) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 5% simple interest?
(5) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(6) How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?
(7) What amount does John have to pay after 6 years if he takes a loan of $3200 at 10% simple interest?
(8) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?
(9) If William paid $3920 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 4% simple interest?