Simple Interest
Math MCQs

Question :    Anthony had to pay $4945 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

Correct Answer  $4300

Solution & Explanation

Solution

Given,

Amount (A) = $4945

Rate of Simple Interest (R) = 5%

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

$4945 = P (1 + 5% × 3)

⇒ $4945 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4945 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4945 = P (1 + ¹⁵/₁₀₀)

⇒ $4945 = P (^{100 + 15}/₁₀₀)

⇒ $4945 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4945

⇒ P = ⁴⁹⁴⁵/_¹¹⁵/100

⇒ P = 4945 × ¹⁰⁰/₁₁₅

⇒ P = ^{4945 × 100}/₁₁₅

⇒ P = ⁴⁹⁴⁵⁰⁰/₁₁₅

⇒ P = $4300

Thus, the sum borrowed (P) = $4300 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 15

Thus, simple interest for 3 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 4945, then the Principal = ¹⁰⁰/₁₁₅ × 4945

= ^{100 × 4945}/₁₁₅

= ⁴⁹⁴⁵⁰⁰/₁₁₅

= 4300

Thus, Principal = $4300

Thus, the sum borrowed = $4300 Answer

Similar Questions

(1) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?

(2) Elizabeth had to pay $3657 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 7 years.

(4) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 4 years.

(5) How much loan did Edward borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9120 to clear it?

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

(7) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 4% simple interest?

(8) How much loan did Michelle borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8340 to clear it?

(9) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 3 years.

(10) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 4% simple interest?