Question:
Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6700
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $12730
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 = $12730 – $6700 = $6030
Thus, Simple Interest = $6030
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 × 6030/6700 × 10
= 603000/67000
= 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) = $6700
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $6030 (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 $6700
= 10/100 × 6700
= 10 × 6700/100
= 67000/100 = 670
Thus, simple Interest for 1 year = $670
Now,
∵ If the simple Interest is $670, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/670 years
∴ If the simple Interest is $6030, then the time = 1/670 × 6030 years
= 1 × 6030/670 years
= 6030/670 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 7% simple interest?
(3) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.
(4) In how much time a principal of $3200 will amount to $3392 at a simple interest of 2% per annum?
(5) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 5% simple interest?
(6) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.
(8) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(9) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 2% simple interest?
(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 4 years.