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 Karen borrowed a sum of $5950 at 4% simple interest for 8 years.

(2) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 5% simple interest?

(3) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.

(5) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 4 years.

(7) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(8) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8692 to clear the loan, then find the time period of the loan.

(9) What amount does John have to pay after 6 years if he takes a loan of $3200 at 9% simple interest?

(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 8 years.