Simple Interest
Math MCQs

Question :    If Barbara paid $3834 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3550

Solution & Explanation

Solution

Given,

Amount (A) = $3834

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

$3834 = P (1 + 2% × 4)

⇒ $3834 = P (1 + ²/₁₀₀ × 4)

⇒ $3834 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3834 = P (1 + ⁸/₁₀₀)

⇒ $3834 = P (^{100 + 8}/₁₀₀)

⇒ $3834 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3834

⇒ P = ³⁸³⁴/_¹⁰⁸/100

⇒ P = 3834 × ¹⁰⁰/₁₀₈

⇒ P = ^{3834 × 100}/₁₀₈

⇒ P = ³⁸³⁴⁰⁰/₁₀₈

⇒ P = $3550

Thus, the sum borrowed (P) = $3550 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 3834, then the Principal = ¹⁰⁰/₁₀₈ × 3834

= ^{100 × 3834}/₁₀₈

= ³⁸³⁴⁰⁰/₁₀₈

= 3550

Thus, Principal = $3550

Thus, the sum borrowed = $3550 Answer

Similar Questions

(1) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 4 years.

(2) How much loan did Anthony borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7560 to clear it?

(3) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.

(4) If Donna paid $5820 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 4 years.

(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 7 years.

(7) If Barbara borrowed $3550 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(8) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.

(9) Barbara had to pay $3976 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) Kenneth had to pay $5600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.