Simple Interest
Math MCQs

Question :    How much loan did Emily borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7762.5 to clear it?

Correct Answer  $6750

Solution & Explanation

Solution

Given,

Amount (A) = $7762.5

Rate of Simple Interest (R) = 3%

Time (T) = 5 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

$7762.5 = P (1 + 3% × 5)

⇒ $7762.5 = P (1 + ³/₁₀₀ × 5)

⇒ $7762.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7762.5 = P (1 + ¹⁵/₁₀₀)

⇒ $7762.5 = P (^{100 + 15}/₁₀₀)

⇒ $7762.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7762.5

⇒ P = ^7762.5/_¹¹⁵/100

⇒ P = 7762.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{7762.5 × 100}/₁₁₅

⇒ P = ⁷⁷⁶²⁵⁰/₁₁₅

⇒ P = $6750

Thus, the sum borrowed (P) = $6750 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 3 = 15

Thus, simple interest for 5 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 7762.5, then the Principal = ¹⁰⁰/₁₁₅ × 7762.5

= ^{100 × 7762.5}/₁₁₅

= ⁷⁷⁶²⁵⁰/₁₁₅

= 6750

Thus, Principal = $6750

Thus, the sum borrowed = $6750 Answer

Similar Questions

(1) 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?

(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.

(3) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 4 years.

(4) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 4 years.

(5) What amount does William have to pay after 6 years if he takes a loan of $3500 at 6% simple interest?

(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 7 years.

(7) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.

(8) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.

(9) How much loan did Ryan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9480 to clear it?

(10) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.