Question : How much loan did John borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5980 to clear it?
Correct Answer $5200
Solution & Explanation
Solution
Given,
Amount (A) = $5980
Rate of Simple Interest (R) = 3%
Time (T) = 5 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
$5980 = P (1 + 3% × 5)
⇒ $5980 = P (1 + 3/100 × 5)
⇒ $5980 = P (1 + 3 × 5/100)
⇒ $5980 = P (1 + 15/100)
⇒ $5980 = P (100 + 15/100)
⇒ $5980 = P × 115/100
⇒ P × 115/100 = $5980
⇒ P = 5980/115/100
⇒ P = 5980 × 100/115
⇒ P = 5980 × 100/115
⇒ P = 598000/115
⇒ P = $5200
Thus, the sum borrowed (P) = $5200 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 = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 3 = 15
Thus, simple interest for 5 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 5980, then the Principal = 100/115 × 5980
= 100 × 5980/115
= 598000/115
= 5200
Thus, Principal = $5200
Thus, the sum borrowed = $5200 Answer
Similar Questions
(1) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?
(2) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 7 years.
(4) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 4 years.
(5) In how much time a principal of $3050 will amount to $3812.5 at a simple interest of 5% per annum?
(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 7 years.
(8) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 9% simple interest?