Question:
Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4200
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $6216
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 = $6216 – $4200 = $2016
Thus, Simple Interest = $2016
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 × 2016/4200 × 6
= 201600/25200
= 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) = $4200
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2016 (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 = 6% of Principal
= 6% of $4200
= 6/100 × 4200
= 6 × 4200/100
= 25200/100 = 252
Thus, simple Interest for 1 year = $252
Now,
∵ If the simple Interest is $252, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/252 years
∴ If the simple Interest is $2016, then the time = 1/252 × 2016 years
= 1 × 2016/252 years
= 2016/252 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 8 years.
(2) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 9% simple interest?
(3) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 4 years.
(5) How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?
(6) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(7) Joshua had to pay $5635 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.
(10) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.