Question:
Daniel had to pay $4715 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
$4100
Solution And Explanation
Solution
Given,
Amount (A) = $4715
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
$4715 = P (1 + 5% × 3)
⇒ $4715 = P (1 + 5/100 × 3)
⇒ $4715 = P (1 + 5 × 3/100)
⇒ $4715 = P (1 + 15/100)
⇒ $4715 = P (100 + 15/100)
⇒ $4715 = P × 115/100
⇒ P × 115/100 = $4715
⇒ P = 4715/115/100
⇒ P = 4715 × 100/115
⇒ P = 4715 × 100/115
⇒ P = 471500/115
⇒ P = $4100
Thus, the sum borrowed (P) = $4100 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 4715, then the Principal = 100/115 × 4715
= 100 × 4715/115
= 471500/115
= 4100
Thus, Principal = $4100
Thus, the sum borrowed = $4100 Answer
Similar Questions
(1) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 4 years.
(2) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 5% simple interest?
(3) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
(5) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 9% simple interest?
(6) James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 6% simple interest?
(8) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 6% simple interest?
(9) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 4% simple interest?
(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 4 years.