Simple Interest
Math MCQs

Question :    Barbara had to pay $3763 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

Correct Answer  $3550

Solution & Explanation

Solution

Given,

Amount (A) = $3763

Rate of Simple Interest (R) = 2%

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

$3763 = P (1 + 2% × 3)

⇒ $3763 = P (1 + ²/₁₀₀ × 3)

⇒ $3763 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $3763 = P (1 + ⁶/₁₀₀)

⇒ $3763 = P (^{100 + 6}/₁₀₀)

⇒ $3763 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $3763

⇒ P = ³⁷⁶³/_¹⁰⁶/100

⇒ P = 3763 × ¹⁰⁰/₁₀₆

⇒ P = ^{3763 × 100}/₁₀₆

⇒ P = ³⁷⁶³⁰⁰/₁₀₆

⇒ P = $3550

Thus, the sum borrowed (P) = $3550 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₆

∴ If the Amount is 3763, then the Principal = ¹⁰⁰/₁₀₆ × 3763

= ^{100 × 3763}/₁₀₆

= ³⁷⁶³⁰⁰/₁₀₆

= 3550

Thus, Principal = $3550

Thus, the sum borrowed = $3550 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.

(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.

(3) Kenneth had to pay $5750 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 8 years.

(5) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 2% simple interest?

(6) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 7% simple interest.

(7) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 9% simple interest.

(8) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 9% simple interest?

(9) How much loan did Robert borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5865 to clear it?

(10) Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.