Question:
How much loan did Ashley borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8187.5 to clear it?
Correct Answer
$6550
Solution And Explanation
Solution
Given,
Amount (A) = $8187.5
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
$8187.5 = P (1 + 5% × 5)
⇒ $8187.5 = P (1 + 5/100 × 5)
⇒ $8187.5 = P (1 + 5 × 5/100)
⇒ $8187.5 = P (1 + 25/100)
⇒ $8187.5 = P (100 + 25/100)
⇒ $8187.5 = P × 125/100
⇒ P × 125/100 = $8187.5
⇒ P = 8187.5/125/100
⇒ P = 8187.5 × 100/125
⇒ P = 8187.5 × 100/125
⇒ P = 818750/125
⇒ P = $6550
Thus, the sum borrowed (P) = $6550 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 8187.5, then the Principal = 100/125 × 8187.5
= 100 × 8187.5/125
= 818750/125
= 6550
Thus, Principal = $6550
Thus, the sum borrowed = $6550 Answer
Similar Questions
(1) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 8 years.
(3) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 8% simple interest?
(4) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.
(5) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 8% simple interest?
(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 8 years.
(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 8 years.
(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.
(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.
(10) How much loan did Karen borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6545 to clear it?