Question:
Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4300
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $7396
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 = $7396 – $4300 = $3096
Thus, Simple Interest = $3096
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 × 3096/4300 × 9
= 309600/38700
= 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) = $4300
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3096 (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 $4300
= 9/100 × 4300
= 9 × 4300/100
= 38700/100 = 387
Thus, simple Interest for 1 year = $387
Now,
∵ If the simple Interest is $387, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/387 years
∴ If the simple Interest is $3096, then the time = 1/387 × 3096 years
= 1 × 3096/387 years
= 3096/387 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 3 years.
(2) William had to pay $3710 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) Richard had to pay $4032 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.
(5) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(6) 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?
(7) What amount does William have to pay after 5 years if he takes a loan of $3500 at 5% simple interest?
(8) If Sandra paid $4806 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 4% simple interest?
(10) If Joshua paid $5488 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.