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 does Sarah have to pay after 6 years if he takes a loan of $3850 at 9% simple interest?
(2) How much loan did Daniel borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6710 to clear it?
(3) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.
(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 3 years.
(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 8 years.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 7 years.
(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 4 years.
(8) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.
(9) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.