Question:
If Michael paid $3564 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3300
Solution And Explanation
Solution
Given,
Amount (A) = $3564
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
$3564 = P (1 + 2% × 4)
⇒ $3564 = P (1 + 2/100 × 4)
⇒ $3564 = P (1 + 2 × 4/100)
⇒ $3564 = P (1 + 8/100)
⇒ $3564 = P (100 + 8/100)
⇒ $3564 = P × 108/100
⇒ P × 108/100 = $3564
⇒ P = 3564/108/100
⇒ P = 3564 × 100/108
⇒ P = 3564 × 100/108
⇒ P = 356400/108
⇒ P = $3300
Thus, the sum borrowed (P) = $3300 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 3564, then the Principal = 100/108 × 3564
= 100 × 3564/108
= 356400/108
= 3300
Thus, Principal = $3300
Thus, the sum borrowed = $3300 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
(2) Charles had to pay $4134 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(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 after 10 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.
(5) How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?
(6) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 8% simple interest?
(7) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 6% simple interest?
(8) How much loan did Jason borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9240 to clear it?
(9) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 7 years.