Simple Interest
Math MCQs

Question :    If Robert paid $3596 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3100

Solution & Explanation

Solution

Given,

Amount (A) = $3596

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

$3596 = P (1 + 4% × 4)

⇒ $3596 = P (1 + ⁴/₁₀₀ × 4)

⇒ $3596 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $3596 = P (1 + ¹⁶/₁₀₀)

⇒ $3596 = P (^{100 + 16}/₁₀₀)

⇒ $3596 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $3596

⇒ P = ³⁵⁹⁶/_¹¹⁶/100

⇒ P = 3596 × ¹⁰⁰/₁₁₆

⇒ P = ^{3596 × 100}/₁₁₆

⇒ P = ³⁵⁹⁶⁰⁰/₁₁₆

⇒ P = $3100

Thus, the sum borrowed (P) = $3100 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 3596, then the Principal = ¹⁰⁰/₁₁₆ × 3596

= ^{100 × 3596}/₁₁₆

= ³⁵⁹⁶⁰⁰/₁₁₆

= 3100

Thus, Principal = $3100

Thus, the sum borrowed = $3100 Answer

Similar Questions

(1) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 7 years.

(3) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 3% simple interest?

(4) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.

(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 3 years.

(6) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 4 years.

(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 4 years.

(9) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 3% simple interest?

(10) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 3% simple interest?