Question:
If Mary paid $3416 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$3050
Solution And Explanation
Solution
Given,
Amount (A) = $3416
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
$3416 = P (1 + 3% × 4)
⇒ $3416 = P (1 + 3/100 × 4)
⇒ $3416 = P (1 + 3 × 4/100)
⇒ $3416 = P (1 + 12/100)
⇒ $3416 = P (100 + 12/100)
⇒ $3416 = P × 112/100
⇒ P × 112/100 = $3416
⇒ P = 3416/112/100
⇒ P = 3416 × 100/112
⇒ P = 3416 × 100/112
⇒ P = 341600/112
⇒ P = $3050
Thus, the sum borrowed (P) = $3050 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 3416, then the Principal = 100/112 × 3416
= 100 × 3416/112
= 341600/112
= 3050
Thus, Principal = $3050
Thus, the sum borrowed = $3050 Answer
Similar Questions
(1) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 8 years.
(2) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(3) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 6% simple interest?
(4) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 7% simple interest.
(5) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 2% simple interest?
(6) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 5% simple interest?
(7) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 10% simple interest?
(8) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.
(10) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.