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) What amount does John have to pay after 5 years if he takes a loan of $3200 at 3% simple interest?
(2) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.
(3) If Matthew paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 9% simple interest?
(5) Richard had to pay $4032 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.
(7) 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.
(8) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.
(9) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?
(10) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?