Simple Interest
Math MCQs

Question :    How much loan did Donna borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7877.5 to clear it?

Correct Answer  $6850

Solution & Explanation

Solution

Given,

Amount (A) = $7877.5

Rate of Simple Interest (R) = 3%

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

$7877.5 = P (1 + 3% × 5)

⇒ $7877.5 = P (1 + ³/₁₀₀ × 5)

⇒ $7877.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7877.5 = P (1 + ¹⁵/₁₀₀)

⇒ $7877.5 = P (^{100 + 15}/₁₀₀)

⇒ $7877.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7877.5

⇒ P = ^7877.5/_¹¹⁵/100

⇒ P = 7877.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{7877.5 × 100}/₁₁₅

⇒ P = ⁷⁸⁷⁷⁵⁰/₁₁₅

⇒ P = $6850

Thus, the sum borrowed (P) = $6850 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 7877.5, then the Principal = ¹⁰⁰/₁₁₅ × 7877.5

= ^{100 × 7877.5}/₁₁₅

= ⁷⁸⁷⁷⁵⁰/₁₁₅

= 6850

Thus, Principal = $6850

Thus, the sum borrowed = $6850 Answer

Similar Questions

(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.

(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 3 years.

(3) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.

(4) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 8 years.

(6) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.

(7) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 4 years.

(8) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 4 years.

(9) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.

(10) 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.