Question:
Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $10800
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 = $10800 – $6000 = $4800
Thus, Simple Interest = $4800
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 × 4800/6000 × 10
= 480000/60000
= 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) = $6000
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4800 (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 = 10% of Principal
= 10% of $6000
= 10/100 × 6000
= 10 × 6000/100
= 60000/100 = 600
Thus, simple Interest for 1 year = $600
Now,
∵ If the simple Interest is $600, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/600 years
∴ If the simple Interest is $4800, then the time = 1/600 × 4800 years
= 1 × 4800/600 years
= 4800/600 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 7 years.
(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 8 years.
(3) How much loan did Deborah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8195 to clear it?
(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 8 years.
(5) How much loan did Paul borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7705 to clear it?
(6) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.
(7) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.
(8) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 10% simple interest?
(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 8 years.
(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.