Question:
Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $10450 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) = 9% per annum
Amount (A) = $10450
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 = $10450 – $5500 = $4950
Thus, Simple Interest = $4950
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 × 4950/5500 × 9
= 495000/49500
= 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) = 9% per annum
Simple Interest = $4950 (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 $5500
= 9/100 × 5500
= 9 × 5500/100
= 49500/100 = 495
Thus, simple Interest for 1 year = $495
Now,
∵ If the simple Interest is $495, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/495 years
∴ If the simple Interest is $4950, then the time = 1/495 × 4950 years
= 1 × 4950/495 years
= 4950/495 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(3) Michelle had to pay $5395.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) How much loan did Melissa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9187.5 to clear it?
(5) How much loan did Sarah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7020 to clear it?
(6) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5995 to clear it?
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 8 years.
(8) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 4 years.
(10) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.