Question:
If Richard paid $3888 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3600
Solution And Explanation
Solution
Given,
Amount (A) = $3888
Rate of Simple Interest (R) = 2%
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
$3888 = P (1 + 2% × 4)
⇒ $3888 = P (1 + 2/100 × 4)
⇒ $3888 = P (1 + 2 × 4/100)
⇒ $3888 = P (1 + 8/100)
⇒ $3888 = P (100 + 8/100)
⇒ $3888 = P × 108/100
⇒ P × 108/100 = $3888
⇒ P = 3888/108/100
⇒ P = 3888 × 100/108
⇒ P = 3888 × 100/108
⇒ P = 388800/108
⇒ P = $3600
Thus, the sum borrowed (P) = $3600 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 3888, then the Principal = 100/108 × 3888
= 100 × 3888/108
= 388800/108
= 3600
Thus, Principal = $3600
Thus, the sum borrowed = $3600 Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.
(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 9% simple interest?
(3) How much loan did Brian borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8640 to clear it?
(4) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(5) Charles had to pay $4134 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(7) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 6% simple interest?
(8) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.
(9) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
(10) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.