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) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.

(2) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.

(3) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.

(4) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8568 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 3 years.

(6) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 5% per annum?

(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 4 years.

(8) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.

(9) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.