Question:
If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4750
Solution And Explanation
Solution
Given,
Amount (A) = $5700
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
$5700 = P (1 + 5% × 4)
⇒ $5700 = P (1 + 5/100 × 4)
⇒ $5700 = P (1 + 5 × 4/100)
⇒ $5700 = P (1 + 20/100)
⇒ $5700 = P (100 + 20/100)
⇒ $5700 = P × 120/100
⇒ P × 120/100 = $5700
⇒ P = 5700/120/100
⇒ P = 5700 × 100/120
⇒ P = 5700 × 100/120
⇒ P = 570000/120
⇒ P = $4750
Thus, the sum borrowed (P) = $4750 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 5700, then the Principal = 100/120 × 5700
= 100 × 5700/120
= 570000/120
= 4750
Thus, Principal = $4750
Thus, the sum borrowed = $4750 Answer
Similar Questions
(1) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 7% simple interest?
(2) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7748 to clear the loan, then find the time period of the loan.
(3) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.
(4) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.
(5) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 9% simple interest?
(6) If Susan paid $4234 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6392 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
(9) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.
(10) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.