Question:
Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7783 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4300
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $7783
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 = $7783 – $4300 = $3483
Thus, Simple Interest = $3483
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 × 3483/4300 × 9
= 348300/38700
= 9 years (using formula)
Thus, Time (T) = 9 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 = $3483 (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 $3483, then the time = 1/387 × 3483 years
= 1 × 3483/387 years
= 3483/387 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 8 years.
(2) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 10% simple interest.
(3) If Ashley paid $5460 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) How much loan did Jacob borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9600 to clear it?
(5) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 9% simple interest?
(6) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 5% simple interest?
(7) Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 3 years.
(10) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 5% simple interest.