Question:
In how much time a principal of $3000 will amount to $3750 at a simple interest of 5% per annum?
Correct Answer
5
Solution And Explanation
Solution
Given,
Principal (P) = $3000
Rate of Simple Interest (R) = 5% per annum
Amount (A) = $3750
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 = $3750 – $3000 = $750
Thus, Simple Interest = $750
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 × 750/3000 × 5
= 75000/15000
= 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) = 5% per annum
Simple Interest = $750 (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 $750, then the time = 1/150 × 750 years
= 1 × 750/150 years
= 750/150 = 5 years
Thus, time (T) = 5 years Answer
Similar Questions
(1) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 8 years.
(2) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.
(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.
(4) How much loan did Margaret borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7302.5 to clear it?
(5) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?
(6) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 6% simple interest?
(7) If Joseph paid $4440 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 4 years.
(10) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.