Question:
If Kimberly paid $5208 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$4650
Solution And Explanation
Solution
Given,
Amount (A) = $5208
Rate of Simple Interest (R) = 3%
Time (T) = 4 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
$5208 = P (1 + 3% × 4)
⇒ $5208 = P (1 + 3/100 × 4)
⇒ $5208 = P (1 + 3 × 4/100)
⇒ $5208 = P (1 + 12/100)
⇒ $5208 = P (100 + 12/100)
⇒ $5208 = P × 112/100
⇒ P × 112/100 = $5208
⇒ P = 5208/112/100
⇒ P = 5208 × 100/112
⇒ P = 5208 × 100/112
⇒ P = 520800/112
⇒ P = $4650
Thus, the sum borrowed (P) = $4650 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
Calculation of the Amount
Since, in the question, time = 4 years
So, we need to calculate the simple interest for the given time period, which is 4 years
Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year
= 4 × 3 = 12
Thus, simple interest for 4 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 5208, then the Principal = 100/112 × 5208
= 100 × 5208/112
= 520800/112
= 4650
Thus, Principal = $4650
Thus, the sum borrowed = $4650 Answer
Similar Questions
(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 4 years.
(2) What amount does James have to pay after 5 years if he takes a loan of $3000 at 2% simple interest?
(3) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 8% simple interest?
(4) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 7 years.
(6) If John borrowed $3200 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 3% simple interest?
(8) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?
(9) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.
(10) If Thomas paid $4408 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.