Question:
In how much time a principal of $3000 will amount to $3450 at a simple interest of 3% per annum?
Correct Answer
5
Solution And Explanation
Solution
Given,
Principal (P) = $3000
Rate of Simple Interest (R) = 3% per annum
Amount (A) = $3450
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 = $3450 – $3000 = $450
Thus, Simple Interest = $450
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 × 450/3000 × 3
= 45000/9000
= 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) = $3000
Rate of Simple Interest (R) = 3% per annum
Simple Interest = $450 (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 $3000
= 3/100 × 3000
= 3 × 3000/100
= 9000/100 = 90
Thus, simple Interest for 1 year = $90
Now,
∵ If the simple Interest is $90, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/90 years
∴ If the simple Interest is $450, then the time = 1/90 × 450 years
= 1 × 450/90 years
= 450/90 = 5 years
Thus, time (T) = 5 years Answer
Similar Questions
(1) In how much time a principal of $3000 will amount to $3750 at a simple interest of 5% per annum?
(2) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.
(3) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 5% simple interest?
(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 8 years.
(5) Joshua had to pay $5194 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) If Richard paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 7 years.
(9) If Jennifer borrowed $3250 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 2% simple interest.