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 9 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.

(2) What amount will be due after 2 years if David borrowed a sum of $3200 at a 10% simple interest?

(3) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 8 years.

(4) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9089 to clear the loan, then find the time period of the loan.

(5) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.

(6) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 6% simple interest?

(7) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 4 years.

(8) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 8 years.

(9) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 3 years.

(10) Sarah had to pay $4427.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.