Question:
If Charles paid $4368 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$3900
Solution And Explanation
Solution
Given,
Amount (A) = $4368
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
$4368 = P (1 + 3% × 4)
⇒ $4368 = P (1 + 3/100 × 4)
⇒ $4368 = P (1 + 3 × 4/100)
⇒ $4368 = P (1 + 12/100)
⇒ $4368 = P (100 + 12/100)
⇒ $4368 = P × 112/100
⇒ P × 112/100 = $4368
⇒ P = 4368/112/100
⇒ P = 4368 × 100/112
⇒ P = 4368 × 100/112
⇒ P = 436800/112
⇒ P = $3900
Thus, the sum borrowed (P) = $3900 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 4368, then the Principal = 100/112 × 4368
= 100 × 4368/112
= 436800/112
= 3900
Thus, Principal = $3900
Thus, the sum borrowed = $3900 Answer
Similar Questions
(1) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 3 years.
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 8 years.
(3) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.
(4) What amount does James have to pay after 5 years if he takes a loan of $3000 at 4% simple interest?
(5) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(7) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.
(8) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?
(9) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 6% simple interest?
(10) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.