Question:
In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?
Correct Answer
3
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (R) = 5% per annum
Amount (A) = $3622.5
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 = $3622.5 – $3150 = $472.5
Thus, Simple Interest = $472.5
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 × 472.5/3150 × 5
= 47250/15750
= 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) = $3150
Rate of Simple Interest (R) = 5% per annum
Simple Interest = $472.5 (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 = 5% of Principal
= 5% of $3150
= 5/100 × 3150
= 5 × 3150/100
= 15750/100 = 157.5
Thus, simple Interest for 1 year = $157.5
Now,
∵ If the simple Interest is $157.5, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/157.5 years
∴ If the simple Interest is $472.5, then the time = 1/157.5 × 472.5 years
= 1 × 472.5/157.5 years
= 472.5/157.5 = 3 years
Thus, time (T) = 3 years Answer
Similar Questions
(1) What amount will be due after 2 years if William borrowed a sum of $3250 at a 7% simple interest?
(2) What amount does David have to pay after 6 years if he takes a loan of $3400 at 9% simple interest?
(3) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.
(4) If Robert paid $3472 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Michael had to pay $3498 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 Patricia borrowed $3150 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 7% simple interest?
(8) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 6% simple interest?
(9) Calculate the amount due if Susan borrowed a sum of $3650 at 4% simple interest for 3 years.
(10) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $12400 to clear the loan, then find the time period of the loan.