Question:
Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $9976
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 = $9976 – $5800 = $4176
Thus, Simple Interest = $4176
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 × 4176/5800 × 9
= 417600/52200
= 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) = $5800
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4176 (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 $4176, then the time = 1/522 × 4176 years
= 1 × 4176/522 years
= 4176/522 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 6% simple interest?
(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 8 years.
(3) What amount does James have to pay after 6 years if he takes a loan of $3000 at 3% simple interest?
(4) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.
(5) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 4% simple interest?
(6) If Nancy paid $4814 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.
(8) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8869 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 7 years.
(10) What amount will be due after 2 years if John borrowed a sum of $3100 at a 8% simple interest?