Question:
How much loan did Michael borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6625 to clear it?
Correct Answer
$5300
Solution And Explanation
Solution
Given,
Amount (A) = $6625
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
$6625 = P (1 + 5% × 5)
⇒ $6625 = P (1 + 5/100 × 5)
⇒ $6625 = P (1 + 5 × 5/100)
⇒ $6625 = P (1 + 25/100)
⇒ $6625 = P (100 + 25/100)
⇒ $6625 = P × 125/100
⇒ P × 125/100 = $6625
⇒ P = 6625/125/100
⇒ P = 6625 × 100/125
⇒ P = 6625 × 100/125
⇒ P = 662500/125
⇒ P = $5300
Thus, the sum borrowed (P) = $5300 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 6625, then the Principal = 100/125 × 6625
= 100 × 6625/125
= 662500/125
= 5300
Thus, Principal = $5300
Thus, the sum borrowed = $5300 Answer
Similar Questions
(1) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 8% simple interest?
(2) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 8% simple interest?
(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 7 years.
(4) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 4 years.
(6) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9437.5 to clear it?
(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 2% simple interest?
(8) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.
(9) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(10) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.