Question:
Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $11210
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 = $11210 – $5900 = $5310
Thus, Simple Interest = $5310
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 × 5310/5900 × 10
= 531000/59000
= 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) = $5900
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $5310 (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 = 10% of Principal
= 10% of $5900
= 10/100 × 5900
= 10 × 5900/100
= 59000/100 = 590
Thus, simple Interest for 1 year = $590
Now,
∵ If the simple Interest is $590, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/590 years
∴ If the simple Interest is $5310, then the time = 1/590 × 5310 years
= 1 × 5310/590 years
= 5310/590 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3584 at a simple interest of 4% per annum?
(2) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.
(3) How much loan did Michelle borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7645 to clear it?
(4) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(5) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.
(6) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.
(8) If Robert borrowed $3100 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 8 years.
(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 8 years.