Question:
Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $11000 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $11000
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 = $11000 – $5500 = $5500
Thus, Simple Interest = $5500
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 × 5500/5500 × 10
= 550000/55000
= 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) = $5500
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $5500 (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 $5500
= 10/100 × 5500
= 10 × 5500/100
= 55000/100 = 550
Thus, simple Interest for 1 year = $550
Now,
∵ If the simple Interest is $550, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/550 years
∴ If the simple Interest is $5500, then the time = 1/550 × 5500 years
= 1 × 5500/550 years
= 5500/550 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.
(2) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 2% simple interest?
(3) How much loan did Matthew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7750 to clear it?
(4) William had to pay $3710 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 7 years.
(6) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.
(8) If Michael paid $3564 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.
(10) How much loan did David borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6210 to clear it?