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) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 8 years.

(2) If Matthew paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) What amount does William have to pay after 5 years if he takes a loan of $3500 at 8% simple interest?

(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 7 years.

(5) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 7 years.

(6) How much loan did Lisa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6957.5 to clear it?

(7) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 7 years.

(9) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 4 years.