Simple Interest
Math MCQs

Question :    How much loan did Rebecca borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9562.5 to clear it?

Correct Answer  $7650

Solution & Explanation

Solution

Given,

Amount (A) = $9562.5

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

$9562.5 = P (1 + 5% × 5)

⇒ $9562.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9562.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9562.5 = P (1 + ²⁵/₁₀₀)

⇒ $9562.5 = P (^{100 + 25}/₁₀₀)

⇒ $9562.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9562.5

⇒ P = ^9562.5/_¹²⁵/100

⇒ P = 9562.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{9562.5 × 100}/₁₂₅

⇒ P = ⁹⁵⁶²⁵⁰/₁₂₅

⇒ P = $7650

Thus, the sum borrowed (P) = $7650 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 9562.5, then the Principal = ¹⁰⁰/₁₂₅ × 9562.5

= ^{100 × 9562.5}/₁₂₅

= ⁹⁵⁶²⁵⁰/₁₂₅

= 7650

Thus, Principal = $7650

Thus, the sum borrowed = $7650 Answer

Similar Questions

(1) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 4 years.

(2) If Charles borrowed $3900 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(3) If Matthew paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(4) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 8% simple interest?

(5) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.

(6) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5995 to clear it?

(7) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.

(8) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 9% simple interest?

(9) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 8% simple interest?

(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 7 years.