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 Robert borrowed a sum of $5100 at 3% simple interest for 8 years.
(2) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 4% simple interest.
(3) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.
(4) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 3 years.
(5) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.
(6) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 2% simple interest?
(7) What amount does William have to pay after 5 years if he takes a loan of $3500 at 3% simple interest?
(8) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(9) Lisa had to pay $4536 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?