Question:
How much loan did Rebecca borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9180 to clear it?
Correct Answer
$7650
Solution And Explanation
Solution
Given,
Amount (A) = $9180
Rate of Simple Interest (R) = 4%
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
$9180 = P (1 + 4% × 5)
⇒ $9180 = P (1 + 4/100 × 5)
⇒ $9180 = P (1 + 4 × 5/100)
⇒ $9180 = P (1 + 20/100)
⇒ $9180 = P (100 + 20/100)
⇒ $9180 = P × 120/100
⇒ P × 120/100 = $9180
⇒ P = 9180/120/100
⇒ P = 9180 × 100/120
⇒ P = 9180 × 100/120
⇒ P = 918000/120
⇒ P = $7650
Thus, the sum borrowed (P) = $7650 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 9180, then the Principal = 100/120 × 9180
= 100 × 9180/120
= 918000/120
= 7650
Thus, Principal = $7650
Thus, the sum borrowed = $7650 Answer
Similar Questions
(1) 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.
(2) Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 8 years.
(3) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 4 years.
(4) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.
(5) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 4 years.
(7) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 4 years.
(8) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 5% simple interest?
(9) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.
(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 7 years.