Question:
How much loan did Michelle borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7645 to clear it?
Correct Answer
$6950
Solution And Explanation
Solution
Given,
Amount (A) = $7645
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
$7645 = P (1 + 2% × 5)
⇒ $7645 = P (1 + 2/100 × 5)
⇒ $7645 = P (1 + 2 × 5/100)
⇒ $7645 = P (1 + 10/100)
⇒ $7645 = P (100 + 10/100)
⇒ $7645 = P × 110/100
⇒ P × 110/100 = $7645
⇒ P = 7645/110/100
⇒ P = 7645 × 100/110
⇒ P = 7645 × 100/110
⇒ P = 764500/110
⇒ P = $6950
Thus, the sum borrowed (P) = $6950 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 7645, then the Principal = 100/110 × 7645
= 100 × 7645/110
= 764500/110
= 6950
Thus, Principal = $6950
Thus, the sum borrowed = $6950 Answer
Similar Questions
(1) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 6% simple interest?
(2) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9238 to clear the loan, then find the time period of the loan.
(3) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 7 years.
(5) Mark had to pay $5060 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 4 years.
(7) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.
(8) If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 7 years.