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) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.

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

(3) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 7% simple interest.

(4) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 7% simple interest?

(5) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 4% simple interest?

(6) How much loan did Mary borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5807.5 to clear it?

(7) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.

(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 8 years.

(9) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.

(10) Karen had to pay $4424 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.