Question:
Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4500
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $7200
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 = $7200 – $4500 = $2700
Thus, Simple Interest = $2700
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 × 2700/4500 × 10
= 270000/45000
= 6 years (using formula)
Thus, Time (T) = 6 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) = 10% per annum
Simple Interest = $2700 (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 = 10% of Principal
= 10% of $4500
= 10/100 × 4500
= 10 × 4500/100
= 45000/100 = 450
Thus, simple Interest for 1 year = $450
Now,
∵ If the simple Interest is $450, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/450 years
∴ If the simple Interest is $2700, then the time = 1/450 × 2700 years
= 1 × 2700/450 years
= 2700/450 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) What amount will be due after 2 years if James borrowed a sum of $3000 at a 6% simple interest?
(2) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 4 years.
(3) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7599 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.
(5) If Jessica paid $4350 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.
(7) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 4 years.
(8) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.
(9) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.
(10) Nancy had to pay $4772.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.