Simple Interest
Math MCQs

Question :    How much loan did Cynthia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9937.5 to clear it?

Correct Answer  $7950

Solution & Explanation

Solution

Given,

Amount (A) = $9937.5

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

$9937.5 = P (1 + 5% × 5)

⇒ $9937.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9937.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9937.5 = P (1 + ²⁵/₁₀₀)

⇒ $9937.5 = P (^{100 + 25}/₁₀₀)

⇒ $9937.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9937.5

⇒ P = ^9937.5/_¹²⁵/100

⇒ P = 9937.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{9937.5 × 100}/₁₂₅

⇒ P = ⁹⁹³⁷⁵⁰/₁₂₅

⇒ P = $7950

Thus, the sum borrowed (P) = $7950 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 9937.5, then the Principal = ¹⁰⁰/₁₂₅ × 9937.5

= ^{100 × 9937.5}/₁₂₅

= ⁹⁹³⁷⁵⁰/₁₂₅

= 7950

Thus, Principal = $7950

Thus, the sum borrowed = $7950 Answer

Similar Questions

(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 7 years.

(2) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 7% simple interest?

(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 7 years.

(4) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 6% simple interest?

(6) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 5% simple interest?

(7) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.

(8) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 4 years.

(10) What amount will be due after 2 years if James borrowed a sum of $3000 at a 8% simple interest?