Question:
If Susan paid $4088 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$3650
Solution And Explanation
Solution
Given,
Amount (A) = $4088
Rate of Simple Interest (R) = 3%
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
$4088 = P (1 + 3% × 4)
⇒ $4088 = P (1 + 3/100 × 4)
⇒ $4088 = P (1 + 3 × 4/100)
⇒ $4088 = P (1 + 12/100)
⇒ $4088 = P (100 + 12/100)
⇒ $4088 = P × 112/100
⇒ P × 112/100 = $4088
⇒ P = 4088/112/100
⇒ P = 4088 × 100/112
⇒ P = 4088 × 100/112
⇒ P = 408800/112
⇒ P = $3650
Thus, the sum borrowed (P) = $3650 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 = 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 × 3 = 12
Thus, simple interest for 4 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 4088, then the Principal = 100/112 × 4088
= 100 × 4088/112
= 408800/112
= 3650
Thus, Principal = $3650
Thus, the sum borrowed = $3650 Answer
Similar Questions
(1) Richard had to pay $4140 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 6% simple interest?
(3) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
(4) If Linda paid $3752 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) William had to pay $3710 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) If Matthew paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) 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.
(8) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(9) How much loan did Ryan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9875 to clear it?
(10) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.