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 Richard have to pay after 6 years if he takes a loan of $3600 at 5% simple interest?
(2) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?
(4) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 3 years.
(5) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 4% simple interest?
(7) How much loan did Karen borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6842.5 to clear it?
(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 3 years.
(9) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 2% simple interest.
(10) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.