Simple Interest
Math MCQs

Question :    If Emily paid $5510 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4750

Solution & Explanation

Solution

Given,

Amount (A) = $5510

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

$5510 = P (1 + 4% × 4)

⇒ $5510 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5510 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5510 = P (1 + ¹⁶/₁₀₀)

⇒ $5510 = P (^{100 + 16}/₁₀₀)

⇒ $5510 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5510

⇒ P = ⁵⁵¹⁰/_¹¹⁶/100

⇒ P = 5510 × ¹⁰⁰/₁₁₆

⇒ P = ^{5510 × 100}/₁₁₆

⇒ P = ⁵⁵¹⁰⁰⁰/₁₁₆

⇒ P = $4750

Thus, the sum borrowed (P) = $4750 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 5510, then the Principal = ¹⁰⁰/₁₁₆ × 5510

= ^{100 × 5510}/₁₁₆

= ⁵⁵¹⁰⁰⁰/₁₁₆

= 4750

Thus, Principal = $4750

Thus, the sum borrowed = $4750 Answer

Similar Questions

(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 8 years.

(2) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 8 years.

(3) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.

(4) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 6% simple interest?

(5) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.

(6) In how much time a principal of $3100 will amount to $3875 at a simple interest of 5% per annum?

(7) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 3 years.

(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 8 years.

(9) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.

(10) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.