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 does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?
(2) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 7 years.
(4) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $14000 to clear the loan, then find the time period of the loan.
(5) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.
(6) How much loan did Sarah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7312.5 to clear it?
(7) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 3 years.
(8) What amount does James have to pay after 6 years if he takes a loan of $3000 at 9% simple interest?
(9) In how much time a principal of $3150 will amount to $3654 at a simple interest of 4% per annum?
(10) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $5848 to clear the loan, then find the time period of the loan.