Question:
In how much time a principal of $3200 will amount to $3680 at a simple interest of 3% per annum?
Correct Answer
5
Solution And Explanation
Solution
Given,
Principal (P) = $3200
Rate of Simple Interest (R) = 3% 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 × 3
= 48000/9600
= 5 years (using formula)
Thus, Time (T) = 5 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) = 3% 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 = 3% of Principal
= 3% of $3200
= 3/100 × 3200
= 3 × 3200/100
= 9600/100 = 96
Thus, simple Interest for 1 year = $96
Now,
∵ If the simple Interest is $96, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/96 years
∴ If the simple Interest is $480, then the time = 1/96 × 480 years
= 1 × 480/96 years
= 480/96 = 5 years
Thus, time (T) = 5 years Answer
Similar Questions
(1) In how much time a principal of $3150 will amount to $3402 at a simple interest of 2% per annum?
(2) If Charles paid $4212 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 4 years.
(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.
(6) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 5% simple interest.
(7) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.
(9) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 7 years.
(10) What amount does John have to pay after 5 years if he takes a loan of $3200 at 5% simple interest?