Simple Interest
Math MCQs

Question :    Linda had to pay $3852.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

Correct Answer  $3350

Solution & Explanation

Solution

Given,

Amount (A) = $3852.5

Rate of Simple Interest (R) = 5%

Time (T) = 3 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

$3852.5 = P (1 + 5% × 3)

⇒ $3852.5 = P (1 + ⁵/₁₀₀ × 3)

⇒ $3852.5 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $3852.5 = P (1 + ¹⁵/₁₀₀)

⇒ $3852.5 = P (^{100 + 15}/₁₀₀)

⇒ $3852.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $3852.5

⇒ P = ^3852.5/_¹¹⁵/100

⇒ P = 3852.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{3852.5 × 100}/₁₁₅

⇒ P = ³⁸⁵²⁵⁰/₁₁₅

⇒ P = $3350

Thus, the sum borrowed (P) = $3350 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 = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 5 = 15

Thus, simple interest for 3 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 3852.5, then the Principal = ¹⁰⁰/₁₁₅ × 3852.5

= ^{100 × 3852.5}/₁₁₅

= ³⁸⁵²⁵⁰/₁₁₅

= 3350

Thus, Principal = $3350

Thus, the sum borrowed = $3350 Answer

Similar Questions

(1) If Patricia borrowed $3150 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(2) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 8 years.

(3) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 8% simple interest?

(4) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.

(5) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.

(6) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 4% simple interest.

(8) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.

(9) Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.