Question:
How much loan did Daniel borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7625 to clear it?
Correct Answer
$6100
Solution And Explanation
Solution
Given,
Amount (A) = $7625
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
$7625 = P (1 + 5% × 5)
⇒ $7625 = P (1 + 5/100 × 5)
⇒ $7625 = P (1 + 5 × 5/100)
⇒ $7625 = P (1 + 25/100)
⇒ $7625 = P (100 + 25/100)
⇒ $7625 = P × 125/100
⇒ P × 125/100 = $7625
⇒ P = 7625/125/100
⇒ P = 7625 × 100/125
⇒ P = 7625 × 100/125
⇒ P = 762500/125
⇒ P = $6100
Thus, the sum borrowed (P) = $6100 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 7625, then the Principal = 100/125 × 7625
= 100 × 7625/125
= 762500/125
= 6100
Thus, Principal = $6100
Thus, the sum borrowed = $6100 Answer
Similar Questions
(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 8 years.
(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.
(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 4 years.
(4) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 6% simple interest?
(5) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 8% simple interest.
(7) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.
(8) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 10% simple interest?
(9) Andrew had to pay $5232 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.