Question:
Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6800
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $10064
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are given
Formual 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 = $10064 – $6800 = $3264
Thus, Simple Interest = $3264
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 × 3264/6800 × 6
= 326400/40800
= 8 years (using formula)
Thus, Time (T) = 8 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) = $6800
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $3264 (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 $6800
= 6/100 × 6800
= 6 × 6800/100
= 40800/100 = 408
Thus, simple Interest for 1 year = $408
Now,
∵ If the simple Interest is $408, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/408 years
∴ If the simple Interest is $3264, then the time = 1/408 × 3264 years
= 1 × 3264/408 years
= 3264/408 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.
(2) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $5984 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 8% simple interest.
(4) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 4 years.
(5) In how much time a principal of $3150 will amount to $3780 at a simple interest of 5% per annum?
(6) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 4 years.
(7) Donna had to pay $5432 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) 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?
(9) How much loan did Steven borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7260 to clear it?
(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 8 years.