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) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 4 years.
(2) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10168 to clear the loan, then find the time period of the loan.
(3) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 2% simple interest?
(4) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 3% simple interest.
(6) What amount will be due after 2 years if David borrowed a sum of $3200 at a 7% simple interest?
(7) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 5% simple interest?
(8) How much loan did Sarah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7020 to clear it?
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 8 years.
(10) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 4 years.