Question:
Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $13110 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) = 9% per annum
Amount (A) = $13110
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 = $13110 – $6900 = $6210
Thus, Simple Interest = $6210
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 × 6210/6900 × 9
= 621000/62100
= 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) = 9% per annum
Simple Interest = $6210 (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 = 9% of Principal
= 9% of $6900
= 9/100 × 6900
= 9 × 6900/100
= 62100/100 = 621
Thus, simple Interest for 1 year = $621
Now,
∵ If the simple Interest is $621, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/621 years
∴ If the simple Interest is $6210, then the time = 1/621 × 6210 years
= 1 × 6210/621 years
= 6210/621 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $10000 to clear the loan, then find the time period of the loan.
(2) If Barbara paid $4118 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) How much loan did Melissa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8085 to clear it?
(4) How much loan did David borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6750 to clear it?
(5) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.
(6) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 9% simple interest?
(7) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?
(8) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.
(10) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.