Question:
James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $6520
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 = $6520 – $4000 = $2520
Thus, Simple Interest = $2520
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 × 2520/4000 × 7
= 252000/28000
= 9 years (using formula)
Thus, Time (T) = 9 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) = $4000
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2520 (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 $4000
= 7/100 × 4000
= 7 × 4000/100
= 28000/100 = 280
Thus, simple Interest for 1 year = $280
Now,
∵ If the simple Interest is $280, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/280 years
∴ If the simple Interest is $2520, then the time = 1/280 × 2520 years
= 1 × 2520/280 years
= 2520/280 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.
(2) How much loan did Joseph borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6555 to clear it?
(3) What amount will be due after 2 years if David borrowed a sum of $3200 at a 7% simple interest?
(4) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 10% simple interest?
(5) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 10% simple interest?
(6) Ashley had to pay $4959.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?
(8) If Kimberly paid $5022 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 3 years.
(10) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.