Simple Interest
Math MCQs

Question :    If Patricia paid $3654 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3150

Solution & Explanation

Solution

Given,

Amount (A) = $3654

Rate of Simple Interest (R) = 4%

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

$3654 = P (1 + 4% × 4)

⇒ $3654 = P (1 + ⁴/₁₀₀ × 4)

⇒ $3654 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $3654 = P (1 + ¹⁶/₁₀₀)

⇒ $3654 = P (^{100 + 16}/₁₀₀)

⇒ $3654 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $3654

⇒ P = ³⁶⁵⁴/_¹¹⁶/100

⇒ P = 3654 × ¹⁰⁰/₁₁₆

⇒ P = ^{3654 × 100}/₁₁₆

⇒ P = ³⁶⁵⁴⁰⁰/₁₁₆

⇒ P = $3150

Thus, the sum borrowed (P) = $3150 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 = 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 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 3654, then the Principal = ¹⁰⁰/₁₁₆ × 3654

= ^{100 × 3654}/₁₁₆

= ³⁶⁵⁴⁰⁰/₁₁₆

= 3150

Thus, Principal = $3150

Thus, the sum borrowed = $3150 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.

(2) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.

(3) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 8 years.

(5) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.

(6) What amount does William have to pay after 5 years if he takes a loan of $3500 at 9% simple interest?

(7) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.

(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 3 years.

(9) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 8% simple interest?

(10) How much loan did Sandra borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8062.5 to clear it?