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) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.
(2) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.
(3) If Joseph paid $4144 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) If Margaret paid $5046 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) What amount does John have to pay after 6 years if he takes a loan of $3200 at 10% simple interest?
(6) Lisa had to pay $4414.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?
(8) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7152 to clear the loan, then find the time period of the loan.
(9) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 8% simple interest?
(10) How much loan did Sarah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7020 to clear it?