Question:
Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $8236
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 = $8236 – $5800 = $2436
Thus, Simple Interest = $2436
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 × 2436/5800 × 6
= 243600/34800
= 7 years (using formula)
Thus, Time (T) = 7 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) = 6% per annum
Simple Interest = $2436 (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 = 6% of Principal
= 6% of $5800
= 6/100 × 5800
= 6 × 5800/100
= 34800/100 = 348
Thus, simple Interest for 1 year = $348
Now,
∵ If the simple Interest is $348, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/348 years
∴ If the simple Interest is $2436, then the time = 1/348 × 2436 years
= 1 × 2436/348 years
= 2436/348 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 4 years.
(2) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.
(4) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 2% simple interest?
(5) What amount does William have to pay after 6 years if he takes a loan of $3500 at 10% simple interest?
(6) Donna had to pay $5286.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(8) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 4% simple interest?
(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 7 years.
(10) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.