Question:
Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $10260
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 = $10260 – $5700 = $4560
Thus, Simple Interest = $4560
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 × 4560/5700 × 10
= 456000/57000
= 8 years (using formula)
Thus, Time (T) = 8 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) = $5700
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4560 (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 $5700
= 10/100 × 5700
= 10 × 5700/100
= 57000/100 = 570
Thus, simple Interest for 1 year = $570
Now,
∵ If the simple Interest is $570, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/570 years
∴ If the simple Interest is $4560, then the time = 1/570 × 4560 years
= 1 × 4560/570 years
= 4560/570 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 10% simple interest?
(2) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 9% simple interest?
(3) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 8% simple interest?
(4) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 3 years.
(5) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 7 years.
(7) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(8) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?
(9) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 5% simple interest.
(10) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?