Question:
Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $4300
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $8600
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 = $8600 – $4300 = $4300
Thus, Simple Interest = $4300
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 × 4300/4300 × 10
= 430000/43000
= 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) = $4300
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4300 (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 $4300
= 10/100 × 4300
= 10 × 4300/100
= 43000/100 = 430
Thus, simple Interest for 1 year = $430
Now,
∵ If the simple Interest is $430, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/430 years
∴ If the simple Interest is $4300, then the time = 1/430 × 4300 years
= 1 × 4300/430 years
= 4300/430 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Matthew had to pay $4830 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) If William borrowed $3500 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(3) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 8 years.
(5) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 8 years.
(7) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 2% simple interest?
(8) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 9% simple interest?
(9) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 6% simple interest?
(10) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.