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) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 6% simple interest?
(2) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.
(3) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.
(4) How much loan did Melissa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8820 to clear it?
(5) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 7 years.
(7) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 3 years.
(9) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 3 years.
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 8 years.