Question:
In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?
Correct Answer
4
Solution And Explanation
Solution
Given,
Principal (P) = $3200
Rate of Simple Interest (R) = 5% per annum
Amount (A) = $3840
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 = $3840 – $3200 = $640
Thus, Simple Interest = $640
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 × 640/3200 × 5
= 64000/16000
= 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) = $3200
Rate of Simple Interest (R) = 5% per annum
Simple Interest = $640 (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 $3200
= 5/100 × 3200
= 5 × 3200/100
= 16000/100 = 160
Thus, simple Interest for 1 year = $160
Now,
∵ If the simple Interest is $160, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/160 years
∴ If the simple Interest is $640, then the time = 1/160 × 640 years
= 1 × 640/160 years
= 640/160 = 4 years
Thus, time (T) = 4 years Answer
Similar Questions
(1) If Karen paid $4424 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.
(3) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 3 years.
(4) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(5) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.
(6) Betty had to pay $4632.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 7% simple interest?
(9) If Richard paid $3888 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) If Michelle paid $5346 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.