Simple Interest
Math MCQs

Question :    How much loan did Melissa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9187.5 to clear it?

Correct Answer  $7350

Solution & Explanation

Solution

Given,

Amount (A) = $9187.5

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

$9187.5 = P (1 + 5% × 5)

⇒ $9187.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9187.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9187.5 = P (1 + ²⁵/₁₀₀)

⇒ $9187.5 = P (^{100 + 25}/₁₀₀)

⇒ $9187.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9187.5

⇒ P = ^9187.5/_¹²⁵/100

⇒ P = 9187.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{9187.5 × 100}/₁₂₅

⇒ P = ⁹¹⁸⁷⁵⁰/₁₂₅

⇒ P = $7350

Thus, the sum borrowed (P) = $7350 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 9187.5, then the Principal = ¹⁰⁰/₁₂₅ × 9187.5

= ^{100 × 9187.5}/₁₂₅

= ⁹¹⁸⁷⁵⁰/₁₂₅

= 7350

Thus, Principal = $7350

Thus, the sum borrowed = $7350 Answer

Similar Questions

(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 3 years.

(2) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.

(3) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.

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

(5) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.

(6) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 9% simple interest?

(7) How much loan did Karen borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6842.5 to clear it?

(8) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.

(9) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $8976 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.