Question:
Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6100
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $10492
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are given
Formual 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 = $10492 – $6100 = $4392
Thus, Simple Interest = $4392
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 × 4392/6100 × 8
= 439200/48800
= 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) = $6100
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $4392 (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 = 8% of Principal
= 8% of $6100
= 8/100 × 6100
= 8 × 6100/100
= 48800/100 = 488
Thus, simple Interest for 1 year = $488
Now,
∵ If the simple Interest is $488, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/488 years
∴ If the simple Interest is $4392, then the time = 1/488 × 4392 years
= 1 × 4392/488 years
= 4392/488 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 8 years.
(2) If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 7 years.
(4) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 7 years.
(6) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?
(7) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10136 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?
(9) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.
(10) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.