Question:
Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6300
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $10269
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 = $10269 – $6300 = $3969
Thus, Simple Interest = $3969
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 × 3969/6300 × 7
= 396900/44100
= 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) = $6300
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3969 (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 $6300
= 7/100 × 6300
= 7 × 6300/100
= 44100/100 = 441
Thus, simple Interest for 1 year = $441
Now,
∵ If the simple Interest is $441, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/441 years
∴ If the simple Interest is $3969, then the time = 1/441 × 3969 years
= 1 × 3969/441 years
= 3969/441 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) How much loan did Donna borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8220 to clear it?
(2) If Emily paid $5320 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 4 years.
(4) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan.
(5) If Elizabeth borrowed $3450 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(6) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.
(7) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 7 years.
(9) How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?
(10) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.