Question:
Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6900
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $11730
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 = $11730 – $6900 = $4830
Thus, Simple Interest = $4830
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 × 4830/6900 × 7
= 483000/48300
= 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) = $6900
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $4830 (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 $6900
= 7/100 × 6900
= 7 × 6900/100
= 48300/100 = 483
Thus, simple Interest for 1 year = $483
Now,
∵ If the simple Interest is $483, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/483 years
∴ If the simple Interest is $4830, then the time = 1/483 × 4830 years
= 1 × 4830/483 years
= 4830/483 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.
(3) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 8% simple interest.
(4) 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.
(5) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 10% simple interest?
(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 8% simple interest for 4 years.
(7) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.
(8) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?
(9) If Mark paid $4928 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.