Question:
In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?
Correct Answer
5
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (R) = 3% per annum
Amount (A) = $3507.5
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 = $3507.5 – $3050 = $457.5
Thus, Simple Interest = $457.5
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 × 457.5/3050 × 3
= 45750/9150
= 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) = $3050
Rate of Simple Interest (R) = 3% per annum
Simple Interest = $457.5 (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 $3050
= 3/100 × 3050
= 3 × 3050/100
= 9150/100 = 91.5
Thus, simple Interest for 1 year = $91.5
Now,
∵ If the simple Interest is $91.5, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/91.5 years
∴ If the simple Interest is $457.5, then the time = 1/91.5 × 457.5 years
= 1 × 457.5/91.5 years
= 457.5/91.5 = 5 years
Thus, time (T) = 5 years Answer
Similar Questions
(1) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.
(2) If Thomas paid $4104 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 after 9 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
(4) How much loan did Ryan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9875 to clear it?
(5) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.
(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 4 years.
(7) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 4 years.
(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 7 years.
(9) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 7 years.
(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 8 years.