Simple Interest
Math MCQs

Question :  ( 1 of 10 )  How much loan did Jennifer borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6037.5 to clear it?

Correct Answer  $5250

Solution & Explanation

Solution

Given,

Amount (A) = $6037.5

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

$6037.5 = P (1 + 3% × 5)

⇒ $6037.5 = P (1 + ³/₁₀₀ × 5)

⇒ $6037.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6037.5 = P (1 + ¹⁵/₁₀₀)

⇒ $6037.5 = P (^{100 + 15}/₁₀₀)

⇒ $6037.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6037.5

⇒ P = ^6037.5/_¹¹⁵/100

⇒ P = 6037.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{6037.5 × 100}/₁₁₅

⇒ P = ⁶⁰³⁷⁵⁰/₁₁₅

⇒ P = $5250

Thus, the sum borrowed (P) = $5250 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 6037.5, then the Principal = ¹⁰⁰/₁₁₅ × 6037.5

= ^{100 × 6037.5}/₁₁₅

= ⁶⁰³⁷⁵⁰/₁₁₅

= 5250

Thus, Principal = $5250

Thus, the sum borrowed = $5250 Answer

Similar Questions

(1) In how much time a principal of $3100 will amount to $3720 at a simple interest of 5% per annum?

(2) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?

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

(4) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.

(5) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 6% simple interest?

(6) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?

(7) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.

(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.

(9) How much loan did Jason borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8470 to clear it?

(10) If James borrowed $3000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.