Simple Interest
Math MCQs

Question :    How much loan did Sarah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7312.5 to clear it?

Correct Answer  $5850

Solution & Explanation

Solution

Given,

Amount (A) = $7312.5

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

$7312.5 = P (1 + 5% × 5)

⇒ $7312.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7312.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7312.5 = P (1 + ²⁵/₁₀₀)

⇒ $7312.5 = P (^{100 + 25}/₁₀₀)

⇒ $7312.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7312.5

⇒ P = ^7312.5/_¹²⁵/100

⇒ P = 7312.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{7312.5 × 100}/₁₂₅

⇒ P = ⁷³¹²⁵⁰/₁₂₅

⇒ P = $5850

Thus, the sum borrowed (P) = $5850 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 7312.5, then the Principal = ¹⁰⁰/₁₂₅ × 7312.5

= ^{100 × 7312.5}/₁₂₅

= ⁷³¹²⁵⁰/₁₂₅

= 5850

Thus, Principal = $5850

Thus, the sum borrowed = $5850 Answer

Similar Questions

(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.

(2) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 7% simple interest.

(4) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?

(5) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 10% simple interest?

(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 8 years.

(8) Calculate the amount due if Barbara borrowed a sum of $3550 at 2% simple interest for 3 years.

(9) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.

(10) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.