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) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 8 years.

(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 7 years.

(3) John had to pay $3392 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 8% simple interest?

(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 8 years.

(6) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.

(7) How much loan did Ashley borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7860 to clear it?

(8) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 3% simple interest?

(9) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% simple interest?

(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 3 years.