Question:
Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6258 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $4200
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $6258
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 = $6258 – $4200 = $2058
Thus, Simple Interest = $2058
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 × 2058/4200 × 7
= 205800/29400
= 7 years (using formula)
Thus, Time (T) = 7 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) = 7% per annum
Simple Interest = $2058 (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 = 7% of Principal
= 7% of $4200
= 7/100 × 4200
= 7 × 4200/100
= 29400/100 = 294
Thus, simple Interest for 1 year = $294
Now,
∵ If the simple Interest is $294, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/294 years
∴ If the simple Interest is $2058, then the time = 1/294 × 2058 years
= 1 × 2058/294 years
= 2058/294 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) How much loan did Joshua borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8625 to clear it?
(2) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 6% simple interest?
(3) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.
(4) In how much time a principal of $3050 will amount to $3812.5 at a simple interest of 5% per annum?
(5) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.
(6) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 3 years.
(8) How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?
(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 8 years.
(10) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.