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

(2) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 3 years.

(3) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 7 years.

(5) What amount does John have to pay after 6 years if he takes a loan of $3200 at 8% simple interest?

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

(7) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?

(8) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.

(9) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(10) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.