Simple Interest
Math MCQs

Question :    How much loan did Patricia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6437.5 to clear it?

Correct Answer  $5150

Solution & Explanation

Solution

Given,

Amount (A) = $6437.5

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

$6437.5 = P (1 + 5% × 5)

⇒ $6437.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $6437.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $6437.5 = P (1 + ²⁵/₁₀₀)

⇒ $6437.5 = P (^{100 + 25}/₁₀₀)

⇒ $6437.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $6437.5

⇒ P = ^6437.5/_¹²⁵/100

⇒ P = 6437.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{6437.5 × 100}/₁₂₅

⇒ P = ⁶⁴³⁷⁵⁰/₁₂₅

⇒ P = $5150

Thus, the sum borrowed (P) = $5150 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 6437.5, then the Principal = ¹⁰⁰/₁₂₅ × 6437.5

= ^{100 × 6437.5}/₁₂₅

= ⁶⁴³⁷⁵⁰/₁₂₅

= 5150

Thus, Principal = $5150

Thus, the sum borrowed = $5150 Answer

Similar Questions

(1) If Christopher paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 8 years.

(3) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 3 years.

(5) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.

(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 7 years.

(7) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8305 to clear it?

(8) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 4 years.

(10) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.