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) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.

(2) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 5% simple interest?

(3) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 8% simple interest?

(4) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.

(5) If Robert borrowed $3100 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(6) David had to pay $3706 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(7) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 6% simple interest?

(9) David had to pay $3604 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 4 years.