Question:
Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6700
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $12060
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 = $12060 – $6700 = $5360
Thus, Simple Interest = $5360
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 × 5360/6700 × 10
= 536000/67000
= 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) = $6700
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $5360 (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 $5360, then the time = 1/670 × 5360 years
= 1 × 5360/670 years
= 5360/670 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.
(2) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 9% simple interest?
(3) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 8% simple interest?
(4) If Robert paid $3472 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 7 years.
(6) How much loan did Andrew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8500 to clear it?
(7) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.
(8) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?
(9) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.
(10) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.