Question:
How much loan did Thomas borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6380 to clear it?
Correct Answer
$5800
Solution And Explanation
Solution
Given,
Amount (A) = $6380
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
$6380 = P (1 + 2% × 5)
⇒ $6380 = P (1 + 2/100 × 5)
⇒ $6380 = P (1 + 2 × 5/100)
⇒ $6380 = P (1 + 10/100)
⇒ $6380 = P (100 + 10/100)
⇒ $6380 = P × 110/100
⇒ P × 110/100 = $6380
⇒ P = 6380/110/100
⇒ P = 6380 × 100/110
⇒ P = 6380 × 100/110
⇒ P = 638000/110
⇒ P = $5800
Thus, the sum borrowed (P) = $5800 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 6380, then the Principal = 100/110 × 6380
= 100 × 6380/110
= 638000/110
= 5800
Thus, Principal = $5800
Thus, the sum borrowed = $5800 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 7% simple interest?
(3) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 4 years.
(4) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.
(5) How much loan did Daniel borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7015 to clear it?
(6) If Barbara borrowed $3550 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 7 years.
(8) Jennifer had to pay $3542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) If Mary borrowed $3050 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(10) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?