Question:
Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
Correct Answer
$4500
Solution And Explanation
Solution
Given,
Amount (A) = $5175
Rate of Simple Interest (R) = 5%
Time (T) = 3 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
$5175 = P (1 + 5% × 3)
⇒ $5175 = P (1 + 5/100 × 3)
⇒ $5175 = P (1 + 5 × 3/100)
⇒ $5175 = P (1 + 15/100)
⇒ $5175 = P (100 + 15/100)
⇒ $5175 = P × 115/100
⇒ P × 115/100 = $5175
⇒ P = 5175/115/100
⇒ P = 5175 × 100/115
⇒ P = 5175 × 100/115
⇒ P = 517500/115
⇒ P = $4500
Thus, the sum borrowed (P) = $4500 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 = 3 years
So, we need to calculate the simple interest for the given time period, which is 3 years
Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year
= 3 × 5 = 15
Thus, simple interest for 3 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 5175, then the Principal = 100/115 × 5175
= 100 × 5175/115
= 517500/115
= 4500
Thus, Principal = $4500
Thus, the sum borrowed = $4500 Answer
Similar Questions
(1) Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 8 years.
(3) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.
(4) Steven had to pay $5290 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) How much loan did Sharon borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8912.5 to clear it?
(6) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 2% simple interest?
(7) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.
(8) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 7% simple interest?
(9) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(10) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.