Question:
Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4100
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $7380
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 = $7380 – $4100 = $3280
Thus, Simple Interest = $3280
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 × 3280/4100 × 10
= 328000/41000
= 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) = $4100
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $3280 (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 = 10% of Principal
= 10% of $4100
= 10/100 × 4100
= 10 × 4100/100
= 41000/100 = 410
Thus, simple Interest for 1 year = $410
Now,
∵ If the simple Interest is $410, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/410 years
∴ If the simple Interest is $3280, then the time = 1/410 × 3280 years
= 1 × 3280/410 years
= 3280/410 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 3 years.
(3) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.
(4) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 8 years.
(6) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 4 years.
(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 3 years.
(9) How much loan did Thomas borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6960 to clear it?
(10) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.