Simple Interest
Math MCQs

Question :    How much loan did Susan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7062.5 to clear it?

Correct Answer  $5650

Solution & Explanation

Solution

Given,

Amount (A) = $7062.5

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

$7062.5 = P (1 + 5% × 5)

⇒ $7062.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7062.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7062.5 = P (1 + ²⁵/₁₀₀)

⇒ $7062.5 = P (^{100 + 25}/₁₀₀)

⇒ $7062.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7062.5

⇒ P = ^7062.5/_¹²⁵/100

⇒ P = 7062.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{7062.5 × 100}/₁₂₅

⇒ P = ⁷⁰⁶²⁵⁰/₁₂₅

⇒ P = $5650

Thus, the sum borrowed (P) = $5650 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 7062.5, then the Principal = ¹⁰⁰/₁₂₅ × 7062.5

= ^{100 × 7062.5}/₁₂₅

= ⁷⁰⁶²⁵⁰/₁₂₅

= 5650

Thus, Principal = $5650

Thus, the sum borrowed = $5650 Answer

Similar Questions

(1) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $11000 to clear the loan, then find the time period of the loan.

(2) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.

(4) How much loan did Betty borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6875 to clear it?

(5) If Linda borrowed $3350 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(6) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.

(7) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6812.5 to clear it?

(8) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $11480 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.

(10) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?