Simple Interest
Math MCQs

Question :    Thomas had to pay $4370 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  $3800

Solution & Explanation

Solution

Given,

Amount (A) = $4370

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

$4370 = P (1 + 5% × 3)

⇒ $4370 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4370 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4370 = P (1 + ¹⁵/₁₀₀)

⇒ $4370 = P (^{100 + 15}/₁₀₀)

⇒ $4370 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4370

⇒ P = ⁴³⁷⁰/_¹¹⁵/100

⇒ P = 4370 × ¹⁰⁰/₁₁₅

⇒ P = ^{4370 × 100}/₁₁₅

⇒ P = ⁴³⁷⁰⁰⁰/₁₁₅

⇒ P = $3800

Thus, the sum borrowed (P) = $3800 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 4370, then the Principal = ¹⁰⁰/₁₁₅ × 4370

= ^{100 × 4370}/₁₁₅

= ⁴³⁷⁰⁰⁰/₁₁₅

= 3800

Thus, Principal = $3800

Thus, the sum borrowed = $3800 Answer

Similar Questions

(1) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 7% simple interest?

(2) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.

(3) Anthony had to pay $4558 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.

(5) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?

(6) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 4 years.

(7) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 9% simple interest?

(8) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 7% simple interest?

(9) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 4 years.