Question:
Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $4600
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $8740
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 = $8740 – $4600 = $4140
Thus, Simple Interest = $4140
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 × 4140/4600 × 9
= 414000/41400
= 10 years (using formula)
Thus, Time (T) = 10 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 = $4140 (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 $4140, then the time = 1/414 × 4140 years
= 1 × 4140/414 years
= 4140/414 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Patricia had to pay $3339 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.
(3) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?
(4) How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?
(5) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 7 years.
(6) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.
(7) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.
(8) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 2% simple interest?
(9) In how much time a principal of $3050 will amount to $3294 at a simple interest of 2% per annum?
(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 2% simple interest for 3 years.