Question:
How much loan did Kimberly borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7647.5 to clear it?
Correct Answer
$6650
Solution And Explanation
Solution
Given,
Amount (A) = $7647.5
Rate of Simple Interest (R) = 3%
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
$7647.5 = P (1 + 3% × 5)
⇒ $7647.5 = P (1 + 3/100 × 5)
⇒ $7647.5 = P (1 + 3 × 5/100)
⇒ $7647.5 = P (1 + 15/100)
⇒ $7647.5 = P (100 + 15/100)
⇒ $7647.5 = P × 115/100
⇒ P × 115/100 = $7647.5
⇒ P = 7647.5/115/100
⇒ P = 7647.5 × 100/115
⇒ P = 7647.5 × 100/115
⇒ P = 764750/115
⇒ 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 7647.5, then the Principal = 100/115 × 7647.5
= 100 × 7647.5/115
= 764750/115
= 6650
Thus, Principal = $6650
Thus, the sum borrowed = $6650 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.
(2) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 2% simple interest?
(3) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.
(4) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.
(6) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.
(7) 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.
(8) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.
(9) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 7% simple interest?
(10) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7980 to clear it?