Question:
Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $8880 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) = 8% per annum
Amount (A) = $8880
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 = $8880 – $6000 = $2880
Thus, Simple Interest = $2880
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 × 2880/6000 × 8
= 288000/48000
= 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) = 8% per annum
Simple Interest = $2880 (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 = 8% of Principal
= 8% of $6000
= 8/100 × 6000
= 8 × 6000/100
= 48000/100 = 480
Thus, simple Interest for 1 year = $480
Now,
∵ If the simple Interest is $480, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/480 years
∴ If the simple Interest is $2880, then the time = 1/480 × 2880 years
= 1 × 2880/480 years
= 2880/480 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.
(2) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.
(3) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 8 years.
(5) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 6% simple interest.
(7) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?
(8) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 3 years.
(9) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 3% simple interest?
(10) How much loan did George borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9125 to clear it?