Question:
How much loan did Karen borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6545 to clear it?
Correct Answer
$5950
Solution And Explanation
Solution
Given,
Amount (A) = $6545
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
$6545 = P (1 + 2% × 5)
⇒ $6545 = P (1 + 2/100 × 5)
⇒ $6545 = P (1 + 2 × 5/100)
⇒ $6545 = P (1 + 10/100)
⇒ $6545 = P (100 + 10/100)
⇒ $6545 = P × 110/100
⇒ P × 110/100 = $6545
⇒ P = 6545/110/100
⇒ P = 6545 × 100/110
⇒ P = 6545 × 100/110
⇒ P = 654500/110
⇒ P = $5950
Thus, the sum borrowed (P) = $5950 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 6545, then the Principal = 100/110 × 6545
= 100 × 6545/110
= 654500/110
= 5950
Thus, Principal = $5950
Thus, the sum borrowed = $5950 Answer
Similar Questions
(1) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 3 years.
(2) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 9% simple interest?
(3) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 7 years.
(5) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 7% simple interest?
(6) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 3 years.
(7) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 7% simple interest?
(8) Margaret had to pay $4741.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 8 years.
(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 4 years.