Simple Interest
Math MCQs

Question :    Jennifer had to pay $3737.5 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  $3250

Solution & Explanation

Solution

Given,

Amount (A) = $3737.5

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

$3737.5 = P (1 + 5% × 3)

⇒ $3737.5 = P (1 + ⁵/₁₀₀ × 3)

⇒ $3737.5 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $3737.5 = P (1 + ¹⁵/₁₀₀)

⇒ $3737.5 = P (^{100 + 15}/₁₀₀)

⇒ $3737.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $3737.5

⇒ P = ^3737.5/_¹¹⁵/100

⇒ P = 3737.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{3737.5 × 100}/₁₁₅

⇒ P = ³⁷³⁷⁵⁰/₁₁₅

⇒ P = $3250

Thus, the sum borrowed (P) = $3250 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 3737.5, then the Principal = ¹⁰⁰/₁₁₅ × 3737.5

= ^{100 × 3737.5}/₁₁₅

= ³⁷³⁷⁵⁰/₁₁₅

= 3250

Thus, Principal = $3250

Thus, the sum borrowed = $3250 Answer

Similar Questions

(1) Calculate the amount due if Susan borrowed a sum of $3650 at 4% simple interest for 3 years.

(2) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.

(3) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 3 years.

(4) Michael had to pay $3696 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

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

(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 3 years.

(7) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.

(8) If Christopher paid $4800 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) In how much time a principal of $3200 will amount to $4000 at a simple interest of 5% per annum?

(10) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 6% simple interest?