Question:
How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8970 to clear it?
Correct Answer
$7800
Solution And Explanation
Solution
Given,
Amount (A) = $8970
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
$8970 = P (1 + 3% × 5)
⇒ $8970 = P (1 + 3/100 × 5)
⇒ $8970 = P (1 + 3 × 5/100)
⇒ $8970 = P (1 + 15/100)
⇒ $8970 = P (100 + 15/100)
⇒ $8970 = P × 115/100
⇒ P × 115/100 = $8970
⇒ P = 8970/115/100
⇒ P = 8970 × 100/115
⇒ P = 8970 × 100/115
⇒ P = 897000/115
⇒ P = $7800
Thus, the sum borrowed (P) = $7800 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 8970, then the Principal = 100/115 × 8970
= 100 × 8970/115
= 897000/115
= 7800
Thus, Principal = $7800
Thus, the sum borrowed = $7800 Answer
Similar Questions
(1) How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?
(2) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 4 years.
(3) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 8% simple interest?
(4) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.
(5) Sandra had to pay $5117.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.
(7) Thomas had to pay $4256 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
(9) Thomas had to pay $4142 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.