Simple Interest
Math MCQs

Question :    Thomas had to pay $4256 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $3800

Solution & Explanation

Solution

Given,

Amount (A) = $4256

Rate of Simple Interest (R) = 4%

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

$4256 = P (1 + 4% × 3)

⇒ $4256 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4256 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $4256 = P (1 + ¹²/₁₀₀)

⇒ $4256 = P (^{100 + 12}/₁₀₀)

⇒ $4256 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4256

⇒ P = ⁴²⁵⁶/_¹¹²/100

⇒ P = 4256 × ¹⁰⁰/₁₁₂

⇒ P = ^{4256 × 100}/₁₁₂

⇒ P = ⁴²⁵⁶⁰⁰/₁₁₂

⇒ P = $3800

Thus, the sum borrowed (P) = $3800 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 12

Thus, simple interest for 3 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 4256, then the Principal = ¹⁰⁰/₁₁₂ × 4256

= ^{100 × 4256}/₁₁₂

= ⁴²⁵⁶⁰⁰/₁₁₂

= 3800

Thus, Principal = $3800

Thus, the sum borrowed = $3800 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.

(2) In how much time a principal of $3150 will amount to $3433.5 at a simple interest of 3% per annum?

(3) In how much time a principal of $3200 will amount to $3392 at a simple interest of 3% per annum?

(4) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.

(5) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.

(6) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.

(7) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.

(9) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?

(10) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 6% simple interest?