Question:
Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11222 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6200
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $11222
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 = $11222 – $6200 = $5022
Thus, Simple Interest = $5022
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 × 5022/6200 × 9
= 502200/55800
= 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) = $6200
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $5022 (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 $6200
= 9/100 × 6200
= 9 × 6200/100
= 55800/100 = 558
Thus, simple Interest for 1 year = $558
Now,
∵ If the simple Interest is $558, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/558 years
∴ If the simple Interest is $5022, then the time = 1/558 × 5022 years
= 1 × 5022/558 years
= 5022/558 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Betty had to pay $4887.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?
(3) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.
(4) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.
(5) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(6) Donald had to pay $4770 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 8 years.
(8) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.
(9) How much loan did Anthony borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6930 to clear it?
(10) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 4% simple interest?