Question:
Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $7000
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $9940
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 = $9940 – $7000 = $2940
Thus, Simple Interest = $2940
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 × 2940/7000 × 7
= 294000/49000
= 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) = $7000
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2940 (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 $7000
= 7/100 × 7000
= 7 × 7000/100
= 49000/100 = 490
Thus, simple Interest for 1 year = $490
Now,
∵ If the simple Interest is $490, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/490 years
∴ If the simple Interest is $2940, then the time = 1/490 × 2940 years
= 1 × 2940/490 years
= 2940/490 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.
(3) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 3% simple interest.
(4) What amount does John have to pay after 5 years if he takes a loan of $3200 at 9% simple interest?
(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 8 years.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 8 years.
(7) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(8) What amount does David have to pay after 6 years if he takes a loan of $3400 at 7% simple interest?
(9) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 4 years.
(10) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.