Question:
If Emily paid $5510 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$4750
Solution And Explanation
Solution
Given,
Amount (A) = $5510
Rate of Simple Interest (R) = 4%
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
$5510 = P (1 + 4% × 4)
⇒ $5510 = P (1 + 4/100 × 4)
⇒ $5510 = P (1 + 4 × 4/100)
⇒ $5510 = P (1 + 16/100)
⇒ $5510 = P (100 + 16/100)
⇒ $5510 = P × 116/100
⇒ P × 116/100 = $5510
⇒ P = 5510/116/100
⇒ P = 5510 × 100/116
⇒ P = 5510 × 100/116
⇒ P = 551000/116
⇒ 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 16
Thus, simple interest for 4 years = 16
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 16 = 116
Calculation of the Principal
Now,
∵ If the Amount is 116, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/116
∴ If the Amount is 5510, then the Principal = 100/116 × 5510
= 100 × 5510/116
= 551000/116
= 4750
Thus, Principal = $4750
Thus, the sum borrowed = $4750 Answer
Similar Questions
(1) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 8% simple interest for 4 years.
(3) Mary had to pay $3233 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?
(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 8 years.
(6) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 6% simple interest?
(7) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.
(8) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 3 years.
(10) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 5% simple interest?