Question:
If Margaret paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4350
Solution And Explanation
Solution
Given,
Amount (A) = $5220
Rate of Simple Interest (R) = 5%
Time (T) = 4 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
$5220 = P (1 + 5% × 4)
⇒ $5220 = P (1 + 5/100 × 4)
⇒ $5220 = P (1 + 5 × 4/100)
⇒ $5220 = P (1 + 20/100)
⇒ $5220 = P (100 + 20/100)
⇒ $5220 = P × 120/100
⇒ P × 120/100 = $5220
⇒ P = 5220/120/100
⇒ P = 5220 × 100/120
⇒ P = 5220 × 100/120
⇒ P = 522000/120
⇒ P = $4350
Thus, the sum borrowed (P) = $4350 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 = 4 years
So, we need to calculate the simple interest for the given time period, which is 4 years
Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year
= 4 × 5 = 20
Thus, simple interest for 4 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 5220, then the Principal = 100/120 × 5220
= 100 × 5220/120
= 522000/120
= 4350
Thus, Principal = $4350
Thus, the sum borrowed = $4350 Answer
Similar Questions
(1) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 8 years.
(3) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 10% simple interest?
(4) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 4 years.
(5) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(6) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 8% simple interest?
(7) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 8 years.
(9) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.
(10) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 2% simple interest?