Simple Interest
Math MCQs

Question :    If Sandra paid $5162 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4450

Solution & Explanation

Solution

Given,

Amount (A) = $5162

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

$5162 = P (1 + 4% × 4)

⇒ $5162 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5162 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5162 = P (1 + ¹⁶/₁₀₀)

⇒ $5162 = P (^{100 + 16}/₁₀₀)

⇒ $5162 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5162

⇒ P = ⁵¹⁶²/_¹¹⁶/100

⇒ P = 5162 × ¹⁰⁰/₁₁₆

⇒ P = ^{5162 × 100}/₁₁₆

⇒ P = ⁵¹⁶²⁰⁰/₁₁₆

⇒ P = $4450

Thus, the sum borrowed (P) = $4450 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 5162, then the Principal = ¹⁰⁰/₁₁₆ × 5162

= ^{100 × 5162}/₁₁₆

= ⁵¹⁶²⁰⁰/₁₁₆

= 4450

Thus, Principal = $4450

Thus, the sum borrowed = $4450 Answer

Similar Questions

(1) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 7 years.

(2) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.

(3) Mark had to pay $5060 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 4% simple interest?

(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 4 years.

(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 4 years.

(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 4 years.

(8) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.

(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 7 years.

(10) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?