Question:
How much loan did Stephanie borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9060 to clear it?
Correct Answer
$7550
Solution And Explanation
Solution
Given,
Amount (A) = $9060
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
$9060 = P (1 + 4% × 5)
⇒ $9060 = P (1 + 4/100 × 5)
⇒ $9060 = P (1 + 4 × 5/100)
⇒ $9060 = P (1 + 20/100)
⇒ $9060 = P (100 + 20/100)
⇒ $9060 = P × 120/100
⇒ P × 120/100 = $9060
⇒ P = 9060/120/100
⇒ P = 9060 × 100/120
⇒ P = 9060 × 100/120
⇒ P = 906000/120
⇒ P = $7550
Thus, the sum borrowed (P) = $7550 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 9060, then the Principal = 100/120 × 9060
= 100 × 9060/120
= 906000/120
= 7550
Thus, Principal = $7550
Thus, the sum borrowed = $7550 Answer
Similar Questions
(1) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 7% simple interest?
(2) If Jennifer borrowed $3250 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(3) Calculate the amount due if Susan borrowed a sum of $3650 at 4% simple interest for 3 years.
(4) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 9% simple interest?
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 7 years.
(6) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 4 years.
(7) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 7% simple interest.
(8) What amount does William have to pay after 5 years if he takes a loan of $3500 at 9% simple interest?
(9) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.
(10) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7748 to clear the loan, then find the time period of the loan.