Simple Interest
Math MCQs

Question :    Linda had to pay $3752 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  $3350

Solution & Explanation

Solution

Given,

Amount (A) = $3752

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

$3752 = P (1 + 4% × 3)

⇒ $3752 = P (1 + ⁴/₁₀₀ × 3)

⇒ $3752 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $3752 = P (1 + ¹²/₁₀₀)

⇒ $3752 = P (^{100 + 12}/₁₀₀)

⇒ $3752 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3752

⇒ P = ³⁷⁵²/_¹¹²/100

⇒ P = 3752 × ¹⁰⁰/₁₁₂

⇒ P = ^{3752 × 100}/₁₁₂

⇒ P = ³⁷⁵²⁰⁰/₁₁₂

⇒ P = $3350

Thus, the sum borrowed (P) = $3350 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 3752, then the Principal = ¹⁰⁰/₁₁₂ × 3752

= ^{100 × 3752}/₁₁₂

= ³⁷⁵²⁰⁰/₁₁₂

= 3350

Thus, Principal = $3350

Thus, the sum borrowed = $3350 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.

(2) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 3 years.

(3) What amount will be due after 2 years if William borrowed a sum of $3250 at a 8% simple interest?

(4) How much loan did Lisa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7260 to clear it?

(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 8 years.

(6) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 3 years.

(7) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.

(8) What amount does John have to pay after 5 years if he takes a loan of $3200 at 9% simple interest?

(9) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 8 years.

(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 8 years.