Question:
How much loan did Daniel borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7625 to clear it?
Correct Answer
$6100
Solution And Explanation
Solution
Given,
Amount (A) = $7625
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
$7625 = P (1 + 5% × 5)
⇒ $7625 = P (1 + 5/100 × 5)
⇒ $7625 = P (1 + 5 × 5/100)
⇒ $7625 = P (1 + 25/100)
⇒ $7625 = P (100 + 25/100)
⇒ $7625 = P × 125/100
⇒ P × 125/100 = $7625
⇒ P = 7625/125/100
⇒ P = 7625 × 100/125
⇒ P = 7625 × 100/125
⇒ P = 762500/125
⇒ P = $6100
Thus, the sum borrowed (P) = $6100 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 7625, then the Principal = 100/125 × 7625
= 100 × 7625/125
= 762500/125
= 6100
Thus, Principal = $6100
Thus, the sum borrowed = $6100 Answer
Similar Questions
(1) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(2) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 4% simple interest?
(3) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 7 years.
(4) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 6% simple interest?
(5) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.
(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 7 years.
(8) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 10% simple interest?
(9) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 9% simple interest?
(10) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6109 to clear the loan, then find the time period of the loan.