Question:
Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7421 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4100
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $7421
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 = $7421 – $4100 = $3321
Thus, Simple Interest = $3321
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 × 3321/4100 × 9
= 332100/36900
= 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) = $4100
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3321 (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 $4100
= 9/100 × 4100
= 9 × 4100/100
= 36900/100 = 369
Thus, simple Interest for 1 year = $369
Now,
∵ If the simple Interest is $369, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/369 years
∴ If the simple Interest is $3321, then the time = 1/369 × 3321 years
= 1 × 3321/369 years
= 3321/369 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Michael had to pay $3597 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 8 years.
(4) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 3 years.
(5) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 7 years.
(7) What amount does James have to pay after 5 years if he takes a loan of $3000 at 3% simple interest?
(8) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 8 years.
(10) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.