Simple Interest
Math MCQs

Question :    How much loan did Betty borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7812.5 to clear it?

Correct Answer  $6250

Solution & Explanation

Solution

Given,

Amount (A) = $7812.5

Rate of Simple Interest (R) = 5%

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

$7812.5 = P (1 + 5% × 5)

⇒ $7812.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7812.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7812.5 = P (1 + ²⁵/₁₀₀)

⇒ $7812.5 = P (^{100 + 25}/₁₀₀)

⇒ $7812.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7812.5

⇒ P = ^7812.5/_¹²⁵/100

⇒ P = 7812.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{7812.5 × 100}/₁₂₅

⇒ P = ⁷⁸¹²⁵⁰/₁₂₅

⇒ P = $6250

Thus, the sum borrowed (P) = $6250 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 = 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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 7812.5, then the Principal = ¹⁰⁰/₁₂₅ × 7812.5

= ^{100 × 7812.5}/₁₂₅

= ⁷⁸¹²⁵⁰/₁₂₅

= 6250

Thus, Principal = $6250

Thus, the sum borrowed = $6250 Answer

Similar Questions

(1) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 4 years.

(2) How much loan did Donald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7800 to clear it?

(3) If Ashley paid $5096 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(4) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 3 years.

(5) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.

(6) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.

(7) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 4% simple interest?

(8) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.

(10) If Christopher paid $4480 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.