Question:
( 1 of 10 ) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
12
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $8424
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 = $8424 – $5400 = $3024
Thus, Simple Interest = $3024
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 × 3024/5400 × 7
= 302400/37800
= 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) = $5400
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3024 (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 = 7% of Principal
= 7% of $5400
= 7/100 × 5400
= 7 × 5400/100
= 37800/100 = 378
Thus, simple Interest for 1 year = $378
Now,
∵ If the simple Interest is $378, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/378 years
∴ If the simple Interest is $3024, then the time = 1/378 × 3024 years
= 1 × 3024/378 years
= 3024/378 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 10% simple interest?
(2) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?
(3) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.
(4) Sarah had to pay $4312 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 4 years.
(6) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 10% simple interest.
(7) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 5% simple interest.
(8) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 2% simple interest.
(10) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 4% simple interest.