Simple Interest
Math MCQs

Question :    How much loan did Nancy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7687.5 to clear it?

Correct Answer  $6150

Solution & Explanation

Solution

Given,

Amount (A) = $7687.5

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

$7687.5 = P (1 + 5% × 5)

⇒ $7687.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7687.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7687.5 = P (1 + ²⁵/₁₀₀)

⇒ $7687.5 = P (^{100 + 25}/₁₀₀)

⇒ $7687.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7687.5

⇒ P = ^7687.5/_¹²⁵/100

⇒ P = 7687.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{7687.5 × 100}/₁₂₅

⇒ P = ⁷⁶⁸⁷⁵⁰/₁₂₅

⇒ P = $6150

Thus, the sum borrowed (P) = $6150 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 7687.5, then the Principal = ¹⁰⁰/₁₂₅ × 7687.5

= ^{100 × 7687.5}/₁₂₅

= ⁷⁶⁸⁷⁵⁰/₁₂₅

= 6150

Thus, Principal = $6150

Thus, the sum borrowed = $6150 Answer

Similar Questions

(1) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 7 years.

(3) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 4 years.

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

(5) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.

(6) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6556 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 7 years.

(8) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 2% simple interest?

(9) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.

(10) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.