Simple Interest
Math MCQs

Question :    If Sandra paid $4806 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4450

Solution & Explanation

Solution

Given,

Amount (A) = $4806

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

$4806 = P (1 + 2% × 4)

⇒ $4806 = P (1 + ²/₁₀₀ × 4)

⇒ $4806 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4806 = P (1 + ⁸/₁₀₀)

⇒ $4806 = P (^{100 + 8}/₁₀₀)

⇒ $4806 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4806

⇒ P = ⁴⁸⁰⁶/_¹⁰⁸/100

⇒ P = 4806 × ¹⁰⁰/₁₀₈

⇒ P = ^{4806 × 100}/₁₀₈

⇒ P = ⁴⁸⁰⁶⁰⁰/₁₀₈

⇒ P = $4450

Thus, the sum borrowed (P) = $4450 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 4806, then the Principal = ¹⁰⁰/₁₀₈ × 4806

= ^{100 × 4806}/₁₀₈

= ⁴⁸⁰⁶⁰⁰/₁₀₈

= 4450

Thus, Principal = $4450

Thus, the sum borrowed = $4450 Answer

Similar Questions

(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.

(2) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 7 years.

(4) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.

(5) Margaret had to pay $4611 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 7 years.

(7) Mark had to pay $4928 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% simple interest?

(9) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $12000 to clear the loan, then find the time period of the loan.

(10) In how much time a principal of $3000 will amount to $3450 at a simple interest of 3% per annum?