Question:
How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?
Correct Answer
$5350
Solution And Explanation
Solution
Given,
Amount (A) = $5885
Rate of Simple Interest (R) = 2%
Time (T) = 5 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
$5885 = P (1 + 2% × 5)
⇒ $5885 = P (1 + 2/100 × 5)
⇒ $5885 = P (1 + 2 × 5/100)
⇒ $5885 = P (1 + 10/100)
⇒ $5885 = P (100 + 10/100)
⇒ $5885 = P × 110/100
⇒ P × 110/100 = $5885
⇒ P = 5885/110/100
⇒ P = 5885 × 100/110
⇒ P = 5885 × 100/110
⇒ P = 588500/110
⇒ P = $5350
Thus, the sum borrowed (P) = $5350 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 = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 5885, then the Principal = 100/110 × 5885
= 100 × 5885/110
= 588500/110
= 5350
Thus, Principal = $5350
Thus, the sum borrowed = $5350 Answer
Similar Questions
(1) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 9% simple interest?
(2) If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?
(4) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10600 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 3 years.
(6) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
(7) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 2% simple interest?
(8) What amount does David have to pay after 5 years if he takes a loan of $3400 at 6% simple interest?
(9) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 4 years.