Question:
How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?
Correct Answer
$6650
Solution And Explanation
Solution
Given,
Amount (A) = $7315
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
$7315 = P (1 + 2% × 5)
⇒ $7315 = P (1 + 2/100 × 5)
⇒ $7315 = P (1 + 2 × 5/100)
⇒ $7315 = P (1 + 10/100)
⇒ $7315 = P (100 + 10/100)
⇒ $7315 = P × 110/100
⇒ P × 110/100 = $7315
⇒ P = 7315/110/100
⇒ P = 7315 × 100/110
⇒ P = 7315 × 100/110
⇒ P = 731500/110
⇒ P = $6650
Thus, the sum borrowed (P) = $6650 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 7315, then the Principal = 100/110 × 7315
= 100 × 7315/110
= 731500/110
= 6650
Thus, Principal = $6650
Thus, the sum borrowed = $6650 Answer
Similar Questions
(1) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9437.5 to clear it?
(2) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.
(3) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 4% simple interest?
(4) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 4 years.
(6) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.
(7) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if William borrowed a sum of $3250 at a 5% simple interest?
(9) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 3 years.
(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 7 years.