Question:
If Donna paid $5432 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$4850
Solution And Explanation
Solution
Given,
Amount (A) = $5432
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
$5432 = P (1 + 3% × 4)
⇒ $5432 = P (1 + 3/100 × 4)
⇒ $5432 = P (1 + 3 × 4/100)
⇒ $5432 = P (1 + 12/100)
⇒ $5432 = P (100 + 12/100)
⇒ $5432 = P × 112/100
⇒ P × 112/100 = $5432
⇒ P = 5432/112/100
⇒ P = 5432 × 100/112
⇒ P = 5432 × 100/112
⇒ P = 543200/112
⇒ P = $4850
Thus, the sum borrowed (P) = $4850 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 5432, then the Principal = 100/112 × 5432
= 100 × 5432/112
= 543200/112
= 4850
Thus, Principal = $4850
Thus, the sum borrowed = $4850 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.
(2) Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(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 Patricia borrowed a sum of $3150 at 7% simple interest for 3 years.
(5) How much loan did Kevin borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8520 to clear it?
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 8 years.
(7) If Jessica borrowed $3750 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(8) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 6% simple interest?
(9) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?
(10) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.