Question:
How much loan did Jason borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9625 to clear it?
Correct Answer
$7700
Solution And Explanation
Solution
Given,
Amount (A) = $9625
Rate of Simple Interest (R) = 5%
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
$9625 = P (1 + 5% × 5)
⇒ $9625 = P (1 + 5/100 × 5)
⇒ $9625 = P (1 + 5 × 5/100)
⇒ $9625 = P (1 + 25/100)
⇒ $9625 = P (100 + 25/100)
⇒ $9625 = P × 125/100
⇒ P × 125/100 = $9625
⇒ P = 9625/125/100
⇒ P = 9625 × 100/125
⇒ P = 9625 × 100/125
⇒ P = 962500/125
⇒ P = $7700
Thus, the sum borrowed (P) = $7700 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 9625, then the Principal = 100/125 × 9625
= 100 × 9625/125
= 962500/125
= 7700
Thus, Principal = $7700
Thus, the sum borrowed = $7700 Answer
Similar Questions
(1) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 4 years.
(2) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(3) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
(4) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 8% simple interest?
(5) Donna had to pay $5286.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 8 years.
(7) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(8) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(9) 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.
(10) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.