Question:
Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7052 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) = 8% per annum
Amount (A) = $7052
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 = $7052 – $4100 = $2952
Thus, Simple Interest = $2952
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 × 2952/4100 × 8
= 295200/32800
= 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) = 8% per annum
Simple Interest = $2952 (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 = 8% of Principal
= 8% of $4100
= 8/100 × 4100
= 8 × 4100/100
= 32800/100 = 328
Thus, simple Interest for 1 year = $328
Now,
∵ If the simple Interest is $328, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/328 years
∴ If the simple Interest is $2952, then the time = 1/328 × 2952 years
= 1 × 2952/328 years
= 2952/328 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) In how much time a principal of $3100 will amount to $3410 at a simple interest of 5% per annum?
(2) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 7 years.
(3) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9360 to clear it?
(4) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.
(5) If Joshua paid $5488 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 8 years.
(7) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 4 years.
(8) Kenneth had to pay $5450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 3 years.
(10) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 8 years.