Simple Interest
Math MCQs

Question :    If Steven paid $5152 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4600

Solution & Explanation

Solution

Given,

Amount (A) = $5152

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

$5152 = P (1 + 3% × 4)

⇒ $5152 = P (1 + ³/₁₀₀ × 4)

⇒ $5152 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $5152 = P (1 + ¹²/₁₀₀)

⇒ $5152 = P (^{100 + 12}/₁₀₀)

⇒ $5152 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5152

⇒ P = ⁵¹⁵²/_¹¹²/100

⇒ P = 5152 × ¹⁰⁰/₁₁₂

⇒ P = ^{5152 × 100}/₁₁₂

⇒ P = ⁵¹⁵²⁰⁰/₁₁₂

⇒ P = $4600

Thus, the sum borrowed (P) = $4600 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 5152, then the Principal = ¹⁰⁰/₁₁₂ × 5152

= ^{100 × 5152}/₁₁₂

= ⁵¹⁵²⁰⁰/₁₁₂

= 4600

Thus, Principal = $4600

Thus, the sum borrowed = $4600 Answer

Similar Questions

(1) How much loan did Mary borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6312.5 to clear it?

(2) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.

(3) Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 4 years.

(4) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 5% simple interest.

(5) How much loan did Thomas borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6960 to clear it?

(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 8 years.

(7) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?

(8) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 4 years.

(9) Donald had to pay $5040 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) What amount does William have to pay after 5 years if he takes a loan of $3500 at 6% simple interest?