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) If Susan paid $3942 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 7 years.

(4) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11584 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 7 years.

(6) What amount does William have to pay after 5 years if he takes a loan of $3500 at 2% simple interest?

(7) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.

(8) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.

(9) If Jessica borrowed $3750 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(10) If Christopher paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.