Question:
Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6700
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $9514
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 = $9514 – $6700 = $2814
Thus, Simple Interest = $2814
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 × 2814/6700 × 7
= 281400/46900
= 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) = $6700
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2814 (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 $6700
= 7/100 × 6700
= 7 × 6700/100
= 46900/100 = 469
Thus, simple Interest for 1 year = $469
Now,
∵ If the simple Interest is $469, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/469 years
∴ If the simple Interest is $2814, then the time = 1/469 × 2814 years
= 1 × 2814/469 years
= 2814/469 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 7 years.
(2) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 2% simple interest?
(3) How much loan did James borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5750 to clear it?
(4) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 4 years.
(5) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.
(6) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.
(7) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 3 years.
(8) In how much time a principal of $3000 will amount to $3360 at a simple interest of 4% per annum?
(9) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 9% simple interest?
(10) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.