Question:
Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $7956
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 = $7956 – $5100 = $2856
Thus, Simple Interest = $2856
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 × 2856/5100 × 7
= 285600/35700
= 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) = $5100
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2856 (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 = 7% of Principal
= 7% of $5100
= 7/100 × 5100
= 7 × 5100/100
= 35700/100 = 357
Thus, simple Interest for 1 year = $357
Now,
∵ If the simple Interest is $357, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/357 years
∴ If the simple Interest is $2856, then the time = 1/357 × 2856 years
= 1 × 2856/357 years
= 2856/357 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
(2) What amount does John have to pay after 6 years if he takes a loan of $3200 at 10% simple interest?
(3) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?
(4) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 3% simple interest?
(5) If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(7) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 7% simple interest?
(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.
(9) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $7888 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.