Question:
Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4600
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $7912
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 = $7912 – $4600 = $3312
Thus, Simple Interest = $3312
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 × 3312/4600 × 9
= 331200/41400
= 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) = $4600
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3312 (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 $4600
= 9/100 × 4600
= 9 × 4600/100
= 41400/100 = 414
Thus, simple Interest for 1 year = $414
Now,
∵ If the simple Interest is $414, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/414 years
∴ If the simple Interest is $3312, then the time = 1/414 × 3312 years
= 1 × 3312/414 years
= 3312/414 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 7 years.
(2) Linda had to pay $3752 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(4) How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?
(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 4 years.
(6) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 7% simple interest?
(7) How much loan did Sharon borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8525 to clear it?
(8) In how much time a principal of $3150 will amount to $3402 at a simple interest of 2% per annum?
(9) In how much time a principal of $3200 will amount to $3520 at a simple interest of 2% per annum?
(10) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10430 to clear the loan, then find the time period of the loan.