Question:
John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4400
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $7568
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 = $7568 – $4400 = $3168
Thus, Simple Interest = $3168
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 × 3168/4400 × 9
= 316800/39600
= 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) = $4400
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3168 (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 $4400
= 9/100 × 4400
= 9 × 4400/100
= 39600/100 = 396
Thus, simple Interest for 1 year = $396
Now,
∵ If the simple Interest is $396, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/396 years
∴ If the simple Interest is $3168, then the time = 1/396 × 3168 years
= 1 × 3168/396 years
= 3168/396 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 9% simple interest?
(2) How much loan did Joshua borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7935 to clear it?
(3) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(4) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(5) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7216 to clear the loan, then find the time period of the loan.
(6) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 7 years.
(8) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 4 years.
(9) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 6% simple interest?
(10) What amount does James have to pay after 6 years if he takes a loan of $3000 at 9% simple interest?