Question : Andrew had to pay $5520 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
Correct Answer $4800
Solution & Explanation
Solution
Given,
Amount (A) = $5520
Rate of Simple Interest (R) = 5%
Time (T) = 3 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
$5520 = P (1 + 5% × 3)
⇒ $5520 = P (1 + 5/100 × 3)
⇒ $5520 = P (1 + 5 × 3/100)
⇒ $5520 = P (1 + 15/100)
⇒ $5520 = P (100 + 15/100)
⇒ $5520 = P × 115/100
⇒ P × 115/100 = $5520
⇒ P = 5520/115/100
⇒ P = 5520 × 100/115
⇒ P = 5520 × 100/115
⇒ P = 552000/115
⇒ P = $4800
Thus, the sum borrowed (P) = $4800 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 = 3 years
So, we need to calculate the simple interest for the given time period, which is 3 years
Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year
= 3 × 5 = 15
Thus, simple interest for 3 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 5520, then the Principal = 100/115 × 5520
= 100 × 5520/115
= 552000/115
= 4800
Thus, Principal = $4800
Thus, the sum borrowed = $4800 Answer
Similar Questions
(4) What amount does David have to pay after 5 years if he takes a loan of $3400 at 5% simple interest?
(5) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 8 years.
(6) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 8% simple interest?
(7) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 7% simple interest?
(8) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 3 years.
(9) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 2% simple interest?