Simple Interest
Math MCQs

Question :    John had to pay $3680 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  $3200

Solution & Explanation

Solution

Given,

Amount (A) = $3680

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

$3680 = P (1 + 5% × 3)

⇒ $3680 = P (1 + ⁵/₁₀₀ × 3)

⇒ $3680 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $3680 = P (1 + ¹⁵/₁₀₀)

⇒ $3680 = P (^{100 + 15}/₁₀₀)

⇒ $3680 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $3680

⇒ P = ³⁶⁸⁰/_¹¹⁵/100

⇒ P = 3680 × ¹⁰⁰/₁₁₅

⇒ P = ^{3680 × 100}/₁₁₅

⇒ P = ³⁶⁸⁰⁰⁰/₁₁₅

⇒ P = $3200

Thus, the sum borrowed (P) = $3200 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 3680, then the Principal = ¹⁰⁰/₁₁₅ × 3680

= ^{100 × 3680}/₁₁₅

= ³⁶⁸⁰⁰⁰/₁₁₅

= 3200

Thus, Principal = $3200

Thus, the sum borrowed = $3200 Answer

Similar Questions

(1) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.

(2) How much loan did Laura borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9420 to clear it?

(3) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 5% simple interest?

(4) How much loan did Jacob borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9600 to clear it?

(5) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 10% simple interest?

(6) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 9% simple interest?

(7) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 9% simple interest?

(8) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 4% simple interest?

(9) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10600 to clear the loan, then find the time period of the loan.

(10) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.