Question:
Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $9204
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 = $9204 – $5900 = $3304
Thus, Simple Interest = $3304
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 × 3304/5900 × 7
= 330400/41300
= 8 years (using formula)
Thus, Time (T) = 8 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) = 7% per annum
Simple Interest = $3304 (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 $5900
= 7/100 × 5900
= 7 × 5900/100
= 41300/100 = 413
Thus, simple Interest for 1 year = $413
Now,
∵ If the simple Interest is $413, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/413 years
∴ If the simple Interest is $3304, then the time = 1/413 × 3304 years
= 1 × 3304/413 years
= 3304/413 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 6% simple interest?
(2) Ashley had to pay $5232.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $8400 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.
(5) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 7 years.
(7) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 6% simple interest?
(8) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 4 years.
(10) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.