Simple Interest
Math MCQs

Question :    If Donna paid $5432 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4850

Solution & Explanation

Solution

Given,

Amount (A) = $5432

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

$5432 = P (1 + 3% × 4)

⇒ $5432 = P (1 + ³/₁₀₀ × 4)

⇒ $5432 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $5432 = P (1 + ¹²/₁₀₀)

⇒ $5432 = P (^{100 + 12}/₁₀₀)

⇒ $5432 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5432

⇒ P = ⁵⁴³²/_¹¹²/100

⇒ P = 5432 × ¹⁰⁰/₁₁₂

⇒ P = ^{5432 × 100}/₁₁₂

⇒ P = ⁵⁴³²⁰⁰/₁₁₂

⇒ P = $4850

Thus, the sum borrowed (P) = $4850 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 5432, then the Principal = ¹⁰⁰/₁₁₂ × 5432

= ^{100 × 5432}/₁₁₂

= ⁵⁴³²⁰⁰/₁₁₂

= 4850

Thus, Principal = $4850

Thus, the sum borrowed = $4850 Answer

Similar Questions

(1) If Charles paid $4680 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 7 years.

(3) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 3% simple interest?

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

(5) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11316 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 8% simple interest?

(7) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 6% simple interest.

(8) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.

(9) If Christopher paid $4800 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.