Question:
If Linda paid $3618 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3350
Solution And Explanation
Solution
Given,
Amount (A) = $3618
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
$3618 = P (1 + 2% × 4)
⇒ $3618 = P (1 + 2/100 × 4)
⇒ $3618 = P (1 + 2 × 4/100)
⇒ $3618 = P (1 + 8/100)
⇒ $3618 = P (100 + 8/100)
⇒ $3618 = P × 108/100
⇒ P × 108/100 = $3618
⇒ P = 3618/108/100
⇒ P = 3618 × 100/108
⇒ P = 3618 × 100/108
⇒ P = 361800/108
⇒ P = $3350
Thus, the sum borrowed (P) = $3350 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 3618, then the Principal = 100/108 × 3618
= 100 × 3618/108
= 361800/108
= 3350
Thus, Principal = $3350
Thus, the sum borrowed = $3350 Answer
Similar Questions
(1) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 3 years.
(2) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.
(3) Steven had to pay $5152 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.
(5) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 7% simple interest?
(6) What amount does William have to pay after 6 years if he takes a loan of $3500 at 4% simple interest?
(7) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 9% simple interest?
(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 8 years.
(9) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.
(10) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.