Question:
Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4500
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $7380
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 = $7380 – $4500 = $2880
Thus, Simple Interest = $2880
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 × 2880/4500 × 8
= 288000/36000
= 8 years (using formula)
Thus, Time (T) = 8 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) = 8% per annum
Simple Interest = $2880 (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 = 8% of Principal
= 8% of $4500
= 8/100 × 4500
= 8 × 4500/100
= 36000/100 = 360
Thus, simple Interest for 1 year = $360
Now,
∵ If the simple Interest is $360, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/360 years
∴ If the simple Interest is $2880, then the time = 1/360 × 2880 years
= 1 × 2880/360 years
= 2880/360 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) If Karen paid $4266 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 3 years.
(3) How much loan did Ashley borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8187.5 to clear it?
(4) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 8% simple interest?
(5) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 3 years.
(6) Matthew had to pay $4830 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) In how much time a principal of $3000 will amount to $3450 at a simple interest of 5% per annum?
(8) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 7% simple interest?
(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 3 years.
(10) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.