Question:
Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4200
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $6468
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 = $6468 – $4200 = $2268
Thus, Simple Interest = $2268
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 × 2268/4200 × 6
= 226800/25200
= 9 years (using formula)
Thus, Time (T) = 9 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 = $2268 (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 $2268, then the time = 1/252 × 2268 years
= 1 × 2268/252 years
= 2268/252 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 8% simple interest.
(2) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 8 years.
(4) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $13000 to clear the loan, then find the time period of the loan.
(5) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8145 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if James borrowed a sum of $3000 at a 8% simple interest?
(7) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?
(8) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 4 years.
(9) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(10) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 6% simple interest?