Question:
Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $9350
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 = $9350 – $5500 = $3850
Thus, Simple Interest = $3850
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 × 3850/5500 × 10
= 385000/55000
= 7 years (using formula)
Thus, Time (T) = 7 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 = $3850 (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 $3850, then the time = 1/550 × 3850 years
= 1 × 3850/550 years
= 3850/550 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(2) If Thomas paid $4408 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 3 years.
(4) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?
(5) How much loan did Robert borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5865 to clear it?
(6) How much loan did Andrew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8500 to clear it?
(7) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 4 years.
(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 8 years.
(9) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 9% simple interest?
(10) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.