Question:
Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4500
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $6390
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 = $6390 – $4500 = $1890
Thus, Simple Interest = $1890
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 × 1890/4500 × 7
= 189000/31500
= 6 years (using formula)
Thus, Time (T) = 6 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) = $4500
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $1890 (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 $4500
= 7/100 × 4500
= 7 × 4500/100
= 31500/100 = 315
Thus, simple Interest for 1 year = $315
Now,
∵ If the simple Interest is $315, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/315 years
∴ If the simple Interest is $1890, then the time = 1/315 × 1890 years
= 1 × 1890/315 years
= 1890/315 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.
(2) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.
(3) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?
(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?
(5) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7240 to clear the loan, then find the time period of the loan.
(6) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
(7) Elizabeth had to pay $3760.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) If Charles borrowed $3900 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(9) How much loan did Michelle borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7992.5 to clear it?
(10) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 2% simple interest.