Question:
In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?
Correct Answer
4
Solution And Explanation
Solution
Given,
Principal (P) = $3200
Rate of Simple Interest (R) = 4% per annum
Amount (A) = $3712
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 = $3712 – $3200 = $512
Thus, Simple Interest = $512
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 × 512/3200 × 4
= 51200/12800
= 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) = 4% per annum
Simple Interest = $512 (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 $3200
= 4/100 × 3200
= 4 × 3200/100
= 12800/100 = 128
Thus, simple Interest for 1 year = $128
Now,
∵ If the simple Interest is $128, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/128 years
∴ If the simple Interest is $512, then the time = 1/128 × 512 years
= 1 × 512/128 years
= 512/128 = 4 years
Thus, time (T) = 4 years Answer
Similar Questions
(1) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.
(2) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.
(4) If Michelle paid $5940 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 3 years.
(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 8 years.
(8) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 3 years.
(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 8 years.