Question:
Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5712 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4200
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $5712
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 = $5712 – $4200 = $1512
Thus, Simple Interest = $1512
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 × 1512/4200 × 6
= 151200/25200
= 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) = $4200
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $1512 (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 $1512, then the time = 1/252 × 1512 years
= 1 × 1512/252 years
= 1512/252 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.
(2) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.
(3) How much loan did Sandra borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7095 to clear it?
(4) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
(5) If Charles borrowed $3900 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(6) What amount will be due after 2 years if David borrowed a sum of $3200 at a 10% simple interest?
(7) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 4 years.
(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 7 years.
(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 3 years.
(10) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.