Simple Interest
Math MCQs

Question :    How much loan did Amanda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8937.5 to clear it?

Correct Answer  $7150

Solution & Explanation

Solution

Given,

Amount (A) = $8937.5

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

$8937.5 = P (1 + 5% × 5)

⇒ $8937.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $8937.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $8937.5 = P (1 + ²⁵/₁₀₀)

⇒ $8937.5 = P (^{100 + 25}/₁₀₀)

⇒ $8937.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $8937.5

⇒ P = ^8937.5/_¹²⁵/100

⇒ P = 8937.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{8937.5 × 100}/₁₂₅

⇒ P = ⁸⁹³⁷⁵⁰/₁₂₅

⇒ P = $7150

Thus, the sum borrowed (P) = $7150 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 8937.5, then the Principal = ¹⁰⁰/₁₂₅ × 8937.5

= ^{100 × 8937.5}/₁₂₅

= ⁸⁹³⁷⁵⁰/₁₂₅

= 7150

Thus, Principal = $7150

Thus, the sum borrowed = $7150 Answer

Similar Questions

(1) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 3% simple interest.

(3) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 8% simple interest?

(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 3 years.

(5) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 7 years.

(7) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.

(8) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 3% simple interest?

(9) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.

(10) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.