Question:
How much loan did Deborah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8195 to clear it?
Correct Answer
$7450
Solution And Explanation
Solution
Given,
Amount (A) = $8195
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
$8195 = P (1 + 2% × 5)
⇒ $8195 = P (1 + 2/100 × 5)
⇒ $8195 = P (1 + 2 × 5/100)
⇒ $8195 = P (1 + 10/100)
⇒ $8195 = P (100 + 10/100)
⇒ $8195 = P × 110/100
⇒ P × 110/100 = $8195
⇒ P = 8195/110/100
⇒ P = 8195 × 100/110
⇒ P = 8195 × 100/110
⇒ P = 819500/110
⇒ P = $7450
Thus, the sum borrowed (P) = $7450 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 8195, then the Principal = 100/110 × 8195
= 100 × 8195/110
= 819500/110
= 7450
Thus, Principal = $7450
Thus, the sum borrowed = $7450 Answer
Similar Questions
(1) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 5% simple interest?
(2) How much loan did Patricia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5922.5 to clear it?
(3) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(4) Jennifer had to pay $3737.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) How much loan did Laura borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8635 to clear it?
(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 7 years.
(7) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.
(8) David had to pay $3808 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 8 years.
(10) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 10% simple interest?