Simple Interest
Math MCQs

Question :    If Linda paid $3752 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3350

Solution & Explanation

Solution

Given,

Amount (A) = $3752

Rate of Simple Interest (R) = 3%

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

$3752 = P (1 + 3% × 4)

⇒ $3752 = P (1 + ³/₁₀₀ × 4)

⇒ $3752 = P (1 + ^{3 × 4}/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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 12

Thus, simple interest for 4 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) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $12400 to clear the loan, then find the time period of the loan.

(2) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 9% simple interest?

(3) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.

(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 8 years.

(5) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.

(6) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 3 years.

(8) Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(9) Andrew had to pay $5376 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) How much loan did Michael borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6360 to clear it?