Question:
Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $9180
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 = $9180 – $5100 = $4080
Thus, Simple Interest = $4080
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 × 4080/5100 × 8
= 408000/40800
= 10 years (using formula)
Thus, Time (T) = 10 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) = $5100
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $4080 (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 $5100
= 8/100 × 5100
= 8 × 5100/100
= 40800/100 = 408
Thus, simple Interest for 1 year = $408
Now,
∵ If the simple Interest is $408, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/408 years
∴ If the simple Interest is $4080, then the time = 1/408 × 4080 years
= 1 × 4080/408 years
= 4080/408 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 3 years.
(2) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 4% simple interest?
(3) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
(4) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?
(5) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 6% simple interest?
(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 4 years.
(7) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.
(8) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9412 to clear the loan, then find the time period of the loan.
(9) If Nancy paid $4814 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.