Question:
How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?
Correct Answer
$5350
Solution And Explanation
Solution
Given,
Amount (A) = $6687.5
Rate of Simple Interest (R) = 5%
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
$6687.5 = P (1 + 5% × 5)
⇒ $6687.5 = P (1 + 5/100 × 5)
⇒ $6687.5 = P (1 + 5 × 5/100)
⇒ $6687.5 = P (1 + 25/100)
⇒ $6687.5 = P (100 + 25/100)
⇒ $6687.5 = P × 125/100
⇒ P × 125/100 = $6687.5
⇒ P = 6687.5/125/100
⇒ P = 6687.5 × 100/125
⇒ P = 6687.5 × 100/125
⇒ P = 668750/125
⇒ P = $5350
Thus, the sum borrowed (P) = $5350 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 6687.5, then the Principal = 100/125 × 6687.5
= 100 × 6687.5/125
= 668750/125
= 5350
Thus, Principal = $5350
Thus, the sum borrowed = $5350 Answer
Similar Questions
(1) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.
(2) Jessica had to pay $4312.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) How much loan did Laura borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9812.5 to clear it?
(4) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 8 years.
(6) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 4% simple interest?
(7) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 10% simple interest.
(8) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.
(9) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 10% simple interest?
(10) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 4 years.