Question:
Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6300
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $10836
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 = $10836 – $6300 = $4536
Thus, Simple Interest = $4536
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 × 4536/6300 × 9
= 453600/56700
= 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) = $6300
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4536 (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 $6300
= 9/100 × 6300
= 9 × 6300/100
= 56700/100 = 567
Thus, simple Interest for 1 year = $567
Now,
∵ If the simple Interest is $567, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/567 years
∴ If the simple Interest is $4536, then the time = 1/567 × 4536 years
= 1 × 4536/567 years
= 4536/567 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Susan had to pay $4197.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 7 years.
(3) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7872 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.
(5) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 4 years.
(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 8 years.
(8) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 8% simple interest?
(9) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 8 years.
(10) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 5% simple interest?