Question:
Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7310 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) = 7% per annum
Amount (A) = $7310
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 = $7310 – $4300 = $3010
Thus, Simple Interest = $3010
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 × 3010/4300 × 7
= 301000/30100
= 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) = 7% per annum
Simple Interest = $3010 (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 $3010, then the time = 1/301 × 3010 years
= 1 × 3010/301 years
= 3010/301 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 3 years.
(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 8 years.
(3) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 8 years.
(5) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 3 years.
(7) Richard had to pay $3924 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 8% simple interest?
(9) How much loan did Michael borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6360 to clear it?
(10) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.