Question:
Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6407 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $4300
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $6407
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 = $6407 – $4300 = $2107
Thus, Simple Interest = $2107
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 × 2107/4300 × 7
= 210700/30100
= 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) = $4300
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2107 (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 = 7% of Principal
= 7% of $4300
= 7/100 × 4300
= 7 × 4300/100
= 30100/100 = 301
Thus, simple Interest for 1 year = $301
Now,
∵ If the simple Interest is $301, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/301 years
∴ If the simple Interest is $2107, then the time = 1/301 × 2107 years
= 1 × 2107/301 years
= 2107/301 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 3 years.
(2) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 6% simple interest?
(3) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 8 years.
(4) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 6% simple interest?
(5) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.
(6) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 3% simple interest?
(7) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?
(8) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 7 years.
(9) James had to pay $3270 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8750 to clear it?