Question:
How much loan did Laura borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9420 to clear it?
Correct Answer
$7850
Solution And Explanation
Solution
Given,
Amount (A) = $9420
Rate of Simple Interest (R) = 4%
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
$9420 = P (1 + 4% × 5)
⇒ $9420 = P (1 + 4/100 × 5)
⇒ $9420 = P (1 + 4 × 5/100)
⇒ $9420 = P (1 + 20/100)
⇒ $9420 = P (100 + 20/100)
⇒ $9420 = P × 120/100
⇒ P × 120/100 = $9420
⇒ P = 9420/120/100
⇒ P = 9420 × 100/120
⇒ P = 9420 × 100/120
⇒ P = 942000/120
⇒ P = $7850
Thus, the sum borrowed (P) = $7850 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 = 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 × 4 = 20
Thus, simple interest for 5 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 9420, then the Principal = 100/120 × 9420
= 100 × 9420/120
= 942000/120
= 7850
Thus, Principal = $7850
Thus, the sum borrowed = $7850 Answer
Similar Questions
(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 7 years.
(2) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 10% simple interest?
(3) What amount does David have to pay after 6 years if he takes a loan of $3400 at 4% simple interest?
(4) Calculate the amount due if Susan borrowed a sum of $3650 at 3% simple interest for 3 years.
(5) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.
(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 8% simple interest for 4 years.
(7) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 8% simple interest.
(8) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 8 years.
(9) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 3% simple interest.
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 7 years.