Question:
( 1 of 10 ) In how much time a principal of $3000 will amount to $3450 at a simple interest of 5% per annum?
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
4.5
Correct Answer
3
Solution And Explanation
Solution
Given,
Principal (P) = $3000
Rate of Simple Interest (R) = 5% 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 × 5
= 45000/15000
= 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) = $3000
Rate of Simple Interest (R) = 5% 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 = 5% of Principal
= 5% of $3000
= 5/100 × 3000
= 5 × 3000/100
= 15000/100 = 150
Thus, simple Interest for 1 year = $150
Now,
∵ If the simple Interest is $150, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/150 years
∴ If the simple Interest is $450, then the time = 1/150 × 450 years
= 1 × 450/150 years
= 450/150 = 3 years
Thus, time (T) = 3 years Answer
Similar Questions
(1) Sarah had to pay $4427.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.
(3) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7647.5 to clear it?
(4) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 7 years.
(6) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 5% simple interest?
(7) In how much time a principal of $3150 will amount to $3780 at a simple interest of 4% per annum?
(8) What amount does David have to pay after 6 years if he takes a loan of $3400 at 8% simple interest?
(9) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 4 years.