Simple Interest
Math MCQs

Question :    Betty had to pay $4760 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $4250

Solution & Explanation

Solution

Given,

Amount (A) = $4760

Rate of Simple Interest (R) = 4%

Time (T) = 3 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

$4760 = P (1 + 4% × 3)

⇒ $4760 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4760 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $4760 = P (1 + ¹²/₁₀₀)

⇒ $4760 = P (^{100 + 12}/₁₀₀)

⇒ $4760 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4760

⇒ P = ⁴⁷⁶⁰/_¹¹²/100

⇒ P = 4760 × ¹⁰⁰/₁₁₂

⇒ P = ^{4760 × 100}/₁₁₂

⇒ P = ⁴⁷⁶⁰⁰⁰/₁₁₂

⇒ P = $4250

Thus, the sum borrowed (P) = $4250 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 = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 4 = 12

Thus, simple interest for 3 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 4760, then the Principal = ¹⁰⁰/₁₁₂ × 4760

= ^{100 × 4760}/₁₁₂

= ⁴⁷⁶⁰⁰⁰/₁₁₂

= 4250

Thus, Principal = $4250

Thus, the sum borrowed = $4250 Answer

Similar Questions

(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 8 years.

(2) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 8% simple interest?

(3) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 4% simple interest?

(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 7 years.

(5) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8400 to clear it?

(6) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?

(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 7 years.

(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 4 years.

(9) How much loan did Michael borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6360 to clear it?

(10) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.