Question:
If Margaret paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$4350
Solution And Explanation
Solution
Given,
Amount (A) = $4698
Rate of Simple Interest (R) = 2%
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
$4698 = P (1 + 2% × 4)
⇒ $4698 = P (1 + 2/100 × 4)
⇒ $4698 = P (1 + 2 × 4/100)
⇒ $4698 = P (1 + 8/100)
⇒ $4698 = P (100 + 8/100)
⇒ $4698 = P × 108/100
⇒ P × 108/100 = $4698
⇒ P = 4698/108/100
⇒ P = 4698 × 100/108
⇒ P = 4698 × 100/108
⇒ P = 469800/108
⇒ P = $4350
Thus, the sum borrowed (P) = $4350 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 4698, then the Principal = 100/108 × 4698
= 100 × 4698/108
= 469800/108
= 4350
Thus, Principal = $4350
Thus, the sum borrowed = $4350 Answer
Similar Questions
(1) What amount does David have to pay after 6 years if he takes a loan of $3400 at 2% simple interest?
(2) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 6% simple interest?
(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 2% simple interest?
(4) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.
(5) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 9% simple interest?
(6) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.
(7) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 10% simple interest.
(8) If Susan borrowed $3650 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(9) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 8% simple interest?
(10) Steven had to pay $4876 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.