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) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
(2) If Daniel paid $4592 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.
(4) Barbara had to pay $4082.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.
(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 8 years.
(7) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 8 years.
(8) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 5% simple interest?
(9) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 7% simple interest?
(10) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.