Question:
In how much time a principal of $3000 will amount to $3480 at a simple interest of 4% per annum?
Correct Answer
4
Solution And Explanation
Solution
Given,
Principal (P) = $3000
Rate of Simple Interest (R) = 4% per annum
Amount (A) = $3480
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 = $3480 – $3000 = $480
Thus, Simple Interest = $480
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 × 480/3000 × 4
= 48000/12000
= 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) = $3000
Rate of Simple Interest (R) = 4% per annum
Simple Interest = $480 (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 $3000
= 4/100 × 3000
= 4 × 3000/100
= 12000/100 = 120
Thus, simple Interest for 1 year = $120
Now,
∵ If the simple Interest is $120, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/120 years
∴ If the simple Interest is $480, then the time = 1/120 × 480 years
= 1 × 480/120 years
= 480/120 = 4 years
Thus, time (T) = 4 years Answer
Similar Questions
(1) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 2% simple interest?
(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 4 years.
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 3 years.
(4) What amount will be due after 2 years if David borrowed a sum of $3200 at a 10% simple interest?
(5) In how much time a principal of $3200 will amount to $3392 at a simple interest of 2% per annum?
(6) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(7) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?
(8) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8750 to clear it?
(9) If Donald paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) John had to pay $3680 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.