Question:
Margaret took a loan of $6700 at the rate of 6% 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
7
Solution And Explanation
Solution
Given,
Principal (P) = $6700
Rate of Simple Interest (R) = 6% 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 × 6
= 281400/40200
= 7 years (using formula)
Thus, Time (T) = 7 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) = 6% 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 = 6% of Principal
= 6% of $6700
= 6/100 × 6700
= 6 × 6700/100
= 40200/100 = 402
Thus, simple Interest for 1 year = $402
Now,
∵ If the simple Interest is $402, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/402 years
∴ If the simple Interest is $2814, then the time = 1/402 × 2814 years
= 1 × 2814/402 years
= 2814/402 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 7 years.
(2) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.
(3) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 4% simple interest?
(4) How much loan did Richard borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6160 to clear it?
(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 3 years.
(6) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.
(7) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?
(8) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 7 years.
(10) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.