Simple Interest
MCQs Math


Question:     If Sarah paid $4158 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.


Correct Answer  $3850

Solution And Explanation

Solution

Given,

Amount (A) = $4158

Rate of Simple Interest (R) = 2%

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

$4158 = P (1 + 2% × 4)

⇒ $4158 = P (1 + 2/100 × 4)

⇒ $4158 = P (1 + 2 × 4/100)

⇒ $4158 = P (1 + 8/100)

⇒ $4158 = P (100 + 8/100)

⇒ $4158 = P × 108/100

⇒ P × 108/100 = $4158

⇒ P = 4158/108/100

⇒ P = 4158 × 100/108

⇒ P = 4158 × 100/108

⇒ P = 415800/108

⇒ P = $3850

Thus, the sum borrowed (P) = $3850 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 = 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 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/108

∴ If the Amount is 4158, then the Principal = 100/108 × 4158

= 100 × 4158/108

= 415800/108

= 3850

Thus, Principal = $3850

Thus, the sum borrowed = $3850 Answer


Similar Questions

(1) David had to pay $3604 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 5% simple interest?

(4) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.

(5) How much loan did Sharon borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8525 to clear it?

(6) Margaret had to pay $5002.5 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 Thomas have to pay after 6 years if he takes a loan of $3800 at 2% simple interest?

(8) If Andrew paid $5184 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.

(10) How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?


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