Question:
In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?
Correct Answer
3
Solution And Explanation
Solution
Given,
Principal (P) = $3200
Rate of Simple Interest (R) = 5% per annum
Amount (A) = $3680
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 = $3680 – $3200 = $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 × 480/3200 × 5
= 48000/16000
= 3 years (using formula)
Thus, Time (T) = 3 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 = $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 = 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 $480, then the time = 1/160 × 480 years
= 1 × 480/160 years
= 480/160 = 3 years
Thus, time (T) = 3 years Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
(3) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.
(4) If Emily paid $5320 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 8 years.
(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 7 years.
(7) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.
(8) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 3% per annum?
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 7 years.
(10) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.