Question:
Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $8160
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 = $8160 – $6000 = $2160
Thus, Simple Interest = $2160
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 × 2160/6000 × 6
= 216000/36000
= 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) = $6000
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2160 (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 $6000
= 6/100 × 6000
= 6 × 6000/100
= 36000/100 = 360
Thus, simple Interest for 1 year = $360
Now,
∵ If the simple Interest is $360, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/360 years
∴ If the simple Interest is $2160, then the time = 1/360 × 2160 years
= 1 × 2160/360 years
= 2160/360 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 7 years.
(3) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 4 years.
(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 8 years.
(5) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 2% simple interest?
(6) How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?
(7) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 5% simple interest?
(9) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 6% simple interest?
(10) Emily had to pay $5035 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.