Question:
How much loan did Mary borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6312.5 to clear it?
Correct Answer
$5050
Solution And Explanation
Solution
Given,
Amount (A) = $6312.5
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
$6312.5 = P (1 + 5% × 5)
⇒ $6312.5 = P (1 + 5/100 × 5)
⇒ $6312.5 = P (1 + 5 × 5/100)
⇒ $6312.5 = P (1 + 25/100)
⇒ $6312.5 = P (100 + 25/100)
⇒ $6312.5 = P × 125/100
⇒ P × 125/100 = $6312.5
⇒ P = 6312.5/125/100
⇒ P = 6312.5 × 100/125
⇒ P = 6312.5 × 100/125
⇒ P = 631250/125
⇒ P = $5050
Thus, the sum borrowed (P) = $5050 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 6312.5, then the Principal = 100/125 × 6312.5
= 100 × 6312.5/125
= 631250/125
= 5050
Thus, Principal = $5050
Thus, the sum borrowed = $5050 Answer
Similar Questions
(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.
(2) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 7 years.
(3) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 3% simple interest?
(4) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 3 years.
(5) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 3 years.
(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 4 years.
(7) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.
(8) If Richard borrowed $3600 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(9) 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.
(10) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 2% simple interest.