Question:
Emily had to pay $5035 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
Correct Answer
$4750
Solution And Explanation
Solution
Given,
Amount (A) = $5035
Rate of Simple Interest (R) = 2%
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
$5035 = P (1 + 2% × 3)
⇒ $5035 = P (1 + 2/100 × 3)
⇒ $5035 = P (1 + 2 × 3/100)
⇒ $5035 = P (1 + 6/100)
⇒ $5035 = P (100 + 6/100)
⇒ $5035 = P × 106/100
⇒ P × 106/100 = $5035
⇒ P = 5035/106/100
⇒ P = 5035 × 100/106
⇒ P = 5035 × 100/106
⇒ P = 503500/106
⇒ P = $4750
Thus, the sum borrowed (P) = $4750 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 6
Thus, simple interest for 3 years = 6
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 6 = 106
Calculation of the Principal
Now,
∵ If the Amount is 106, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/106
∴ If the Amount is 5035, then the Principal = 100/106 × 5035
= 100 × 5035/106
= 503500/106
= 4750
Thus, Principal = $4750
Thus, the sum borrowed = $4750 Answer
Similar Questions
(1) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 9% simple interest?
(2) Michael had to pay $3597 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 4 years.
(4) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 6% simple interest?
(5) If Sarah borrowed $3850 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 8 years.
(7) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.
(8) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?
(9) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 2% simple interest?
(10) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 3% simple interest?