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) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 8 years.
(3) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 4 years.
(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 3 years.
(5) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 3% simple interest?
(6) If Karen paid $4582 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 6% simple interest?
(8) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 4% simple interest?
(9) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 7 years.
(10) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7599 to clear the loan, then find the time period of the loan.