Simple Interest
Math MCQs

Question :    How much loan did Paul borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7705 to clear it?

Correct Answer  $6700

Solution & Explanation

Solution

Given,

Amount (A) = $7705

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

$7705 = P (1 + 3% × 5)

⇒ $7705 = P (1 + ³/₁₀₀ × 5)

⇒ $7705 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7705 = P (1 + ¹⁵/₁₀₀)

⇒ $7705 = P (^{100 + 15}/₁₀₀)

⇒ $7705 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7705

⇒ P = ⁷⁷⁰⁵/_¹¹⁵/100

⇒ P = 7705 × ¹⁰⁰/₁₁₅

⇒ P = ^{7705 × 100}/₁₁₅

⇒ P = ⁷⁷⁰⁵⁰⁰/₁₁₅

⇒ P = $6700

Thus, the sum borrowed (P) = $6700 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 7705, then the Principal = ¹⁰⁰/₁₁₅ × 7705

= ^{100 × 7705}/₁₁₅

= ⁷⁷⁰⁵⁰⁰/₁₁₅

= 6700

Thus, Principal = $6700

Thus, the sum borrowed = $6700 Answer

Similar Questions

(1) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.

(2) What amount will be due after 2 years if David borrowed a sum of $3200 at a 4% simple interest?

(3) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 3 years.

(4) How much loan did Jacob borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $10000 to clear it?

(5) If Matthew paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 4 years.

(7) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.

(9) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 4 years.