Question:
( 1 of 10 ) 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.
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
15
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) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 4 years.
(2) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?
(3) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.
(4) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 10% simple interest?
(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 4 years.
(6) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.
(7) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 7 years.
(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 4 years.
(10) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.