Question:
Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11800 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $11800
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 = $11800 – $5900 = $5900
Thus, Simple Interest = $5900
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 × 5900/5900 × 10
= 590000/59000
= 10 years (using formula)
Thus, Time (T) = 10 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 = $5900 (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 $5900, then the time = 1/590 × 5900 years
= 1 × 5900/590 years
= 5900/590 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 8 years.
(2) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(3) Barbara had to pay $3976 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) What amount does John have to pay after 6 years if he takes a loan of $3200 at 4% simple interest?
(5) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 6% simple interest?
(6) How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?
(7) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 3 years.
(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.
(10) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.