Question:
How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?
Correct Answer
$8000
Solution And Explanation
Solution
Given,
Amount (A) = $9200
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
$9200 = P (1 + 3% × 5)
⇒ $9200 = P (1 + 3/100 × 5)
⇒ $9200 = P (1 + 3 × 5/100)
⇒ $9200 = P (1 + 15/100)
⇒ $9200 = P (100 + 15/100)
⇒ $9200 = P × 115/100
⇒ P × 115/100 = $9200
⇒ P = 9200/115/100
⇒ P = 9200 × 100/115
⇒ P = 9200 × 100/115
⇒ P = 920000/115
⇒ P = $8000
Thus, the sum borrowed (P) = $8000 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 9200, then the Principal = 100/115 × 9200
= 100 × 9200/115
= 920000/115
= 8000
Thus, Principal = $8000
Thus, the sum borrowed = $8000 Answer
Similar Questions
(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 7 years.
(2) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 3 years.
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.
(5) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 7 years.
(6) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 7 years.
(8) What amount does John have to pay after 6 years if he takes a loan of $3200 at 2% simple interest?
(9) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $5984 to clear the loan, then find the time period of the loan.
(10) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 9% simple interest?