Question:
Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $8932
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 = $8932 – $5800 = $3132
Thus, Simple Interest = $3132
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 × 3132/5800 × 9
= 313200/52200
= 6 years (using formula)
Thus, Time (T) = 6 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) = $5800
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3132 (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 = 9% of Principal
= 9% of $5800
= 9/100 × 5800
= 9 × 5800/100
= 52200/100 = 522
Thus, simple Interest for 1 year = $522
Now,
∵ If the simple Interest is $522, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/522 years
∴ If the simple Interest is $3132, then the time = 1/522 × 3132 years
= 1 × 3132/522 years
= 3132/522 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?
(2) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.
(3) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 7 years.
(5) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 7% simple interest?
(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 7 years.
(7) 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.
(8) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.
(9) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 4 years.
(10) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.