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) What amount does William have to pay after 6 years if he takes a loan of $3500 at 7% simple interest?
(2) How much loan did Jessica borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6900 to clear it?
(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 7 years.
(4) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 8% simple interest?
(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 8 years.
(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 8 years.
(7) If Mary borrowed $3050 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(8) What amount does William have to pay after 6 years if he takes a loan of $3500 at 10% simple interest?
(9) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 4 years.
(10) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.