Simple Interest
Math MCQs

Question :  ( 1 of 10 )  How much loan did Stephanie borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9437.5 to clear it?

Correct Answer  $7550

Solution & Explanation

Solution

Given,

Amount (A) = $9437.5

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

$9437.5 = P (1 + 5% × 5)

⇒ $9437.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9437.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9437.5 = P (1 + ²⁵/₁₀₀)

⇒ $9437.5 = P (^{100 + 25}/₁₀₀)

⇒ $9437.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9437.5

⇒ P = ^9437.5/_¹²⁵/100

⇒ P = 9437.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{9437.5 × 100}/₁₂₅

⇒ P = ⁹⁴³⁷⁵⁰/₁₂₅

⇒ P = $7550

Thus, the sum borrowed (P) = $7550 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 9437.5, then the Principal = ¹⁰⁰/₁₂₅ × 9437.5

= ^{100 × 9437.5}/₁₂₅

= ⁹⁴³⁷⁵⁰/₁₂₅

= 7550

Thus, Principal = $7550

Thus, the sum borrowed = $7550 Answer

Similar Questions

(1) How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?

(2) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?

(3) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.

(4) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.

(6) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 8% simple interest?

(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 8 years.

(8) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(9) In how much time a principal of $3050 will amount to $3416 at a simple interest of 3% per annum?

(10) How much loan did Donald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7800 to clear it?