Question:
Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $4500
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $8550
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 = $8550 – $4500 = $4050
Thus, Simple Interest = $4050
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 × 4050/4500 × 9
= 405000/40500
= 10 years (using formula)
Thus, Time (T) = 10 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) = $4500
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4050 (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 = 9% of Principal
= 9% of $4500
= 9/100 × 4500
= 9 × 4500/100
= 40500/100 = 405
Thus, simple Interest for 1 year = $405
Now,
∵ If the simple Interest is $405, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/405 years
∴ If the simple Interest is $4050, then the time = 1/405 × 4050 years
= 1 × 4050/405 years
= 4050/405 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10168 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 7 years.
(4) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.
(6) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.
(7) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 4 years.
(8) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8692 to clear the loan, then find the time period of the loan.
(9) How much loan did Timothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9250 to clear it?
(10) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?