Question:
If Susan paid $3942 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3650
Solution And Explanation
Solution
Given,
Amount (A) = $3942
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
$3942 = P (1 + 2% × 4)
⇒ $3942 = P (1 + 2/100 × 4)
⇒ $3942 = P (1 + 2 × 4/100)
⇒ $3942 = P (1 + 8/100)
⇒ $3942 = P (100 + 8/100)
⇒ $3942 = P × 108/100
⇒ P × 108/100 = $3942
⇒ P = 3942/108/100
⇒ P = 3942 × 100/108
⇒ P = 3942 × 100/108
⇒ P = 394200/108
⇒ P = $3650
Thus, the sum borrowed (P) = $3650 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 3942, then the Principal = 100/108 × 3942
= 100 × 3942/108
= 394200/108
= 3650
Thus, Principal = $3650
Thus, the sum borrowed = $3650 Answer
Similar Questions
(1) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 2% simple interest?
(2) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.
(3) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 6% simple interest?
(4) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 9% simple interest.
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 4% simple interest for 3 years.
(6) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 9% simple interest?
(7) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 3% simple interest?
(8) If Richard paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) How much loan did Ronald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8250 to clear it?
(10) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 8% simple interest?