Question:
How much loan did Linda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6152.5 to clear it?
Correct Answer
$5350
Solution And Explanation
Solution
Given,
Amount (A) = $6152.5
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
$6152.5 = P (1 + 3% × 5)
⇒ $6152.5 = P (1 + 3/100 × 5)
⇒ $6152.5 = P (1 + 3 × 5/100)
⇒ $6152.5 = P (1 + 15/100)
⇒ $6152.5 = P (100 + 15/100)
⇒ $6152.5 = P × 115/100
⇒ P × 115/100 = $6152.5
⇒ P = 6152.5/115/100
⇒ P = 6152.5 × 100/115
⇒ P = 6152.5 × 100/115
⇒ P = 615250/115
⇒ P = $5350
Thus, the sum borrowed (P) = $5350 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 6152.5, then the Principal = 100/115 × 6152.5
= 100 × 6152.5/115
= 615250/115
= 5350
Thus, Principal = $5350
Thus, the sum borrowed = $5350 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(2) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.
(3) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 2% simple interest?
(4) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5680 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 2% simple interest.
(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 7 years.
(7) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.
(8) What amount does William have to pay after 6 years if he takes a loan of $3500 at 5% simple interest?
(9) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.
(10) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 3% simple interest?