Question:
How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?
Correct Answer
$8000
Solution And Explanation
Solution
Given,
Amount (A) = $9200
Rate of Simple Interest (R) = 3%
Time (T) = 5 years
Thus, Principal (P) = ?
Method (1) Using Formula
Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given
Formula to find the Principal (P)
Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)
⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]
⇒ A = P (1 + RT)
Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given
In the given question, we need to find the Principal (P)
Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get
$9200 = P (1 + 3% × 5)
⇒ $9200 = P (1 + 3/100 × 5)
⇒ $9200 = P (1 + 3 × 5/100)
⇒ $9200 = P (1 + 15/100)
⇒ $9200 = P (100 + 15/100)
⇒ $9200 = P × 115/100
⇒ P × 115/100 = $9200
⇒ P = 9200/115/100
⇒ P = 9200 × 100/115
⇒ P = 9200 × 100/115
⇒ P = 920000/115
⇒ P = $8000
Thus, the sum borrowed (P) = $8000 Answer
Method (1) Using Unitary Method
Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given
Calculation of the Simple Interest
Let, the principal = 100
Here, since rate of simple interest = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
Calculation of the Amount
Since, in the question, time = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 9200, then the Principal = 100/115 × 9200
= 100 × 9200/115
= 920000/115
= 8000
Thus, Principal = $8000
Thus, the sum borrowed = $8000 Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 5% simple interest?
(3) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 4 years.
(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 Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?
(6) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(7) How much loan did James borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5500 to clear it?
(8) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 5% simple interest?
(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 7 years.