Question:
Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6600
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $10164
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 = $10164 – $6600 = $3564
Thus, Simple Interest = $3564
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 × 3564/6600 × 6
= 356400/39600
= 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) = $6600
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $3564 (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 $6600
= 6/100 × 6600
= 6 × 6600/100
= 39600/100 = 396
Thus, simple Interest for 1 year = $396
Now,
∵ If the simple Interest is $396, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/396 years
∴ If the simple Interest is $3564, then the time = 1/396 × 3564 years
= 1 × 3564/396 years
= 3564/396 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 7% simple interest?
(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 7 years.
(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 8 years.
(4) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.
(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 4 years.
(6) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 4% simple interest?
(7) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.
(8) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 7% simple interest?
(9) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 2% simple interest?
(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 3 years.