Question:
Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $10148
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 = $10148 – $5900 = $4248
Thus, Simple Interest = $4248
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 × 4248/5900 × 8
= 424800/47200
= 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) = $5900
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $4248 (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 $5900
= 8/100 × 5900
= 8 × 5900/100
= 47200/100 = 472
Thus, simple Interest for 1 year = $472
Now,
∵ If the simple Interest is $472, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/472 years
∴ If the simple Interest is $4248, then the time = 1/472 × 4248 years
= 1 × 4248/472 years
= 4248/472 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.
(2) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 4% simple interest?
(3) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
(4) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?
(5) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.
(6) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.
(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?
(8) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.
(9) If Christopher paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.