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) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.
(2) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 5% simple interest?
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 8 years.
(4) Mary had to pay $3324.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 8% simple interest?
(6) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 8 years.
(8) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 4 years.
(9) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.
(10) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.