Simple Interest
Math MCQs

Question :    Sandra had to pay $4984 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $4450

Solution & Explanation

Solution

Given,

Amount (A) = $4984

Rate of Simple Interest (R) = 4%

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

$4984 = P (1 + 4% × 3)

⇒ $4984 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4984 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $4984 = P (1 + ¹²/₁₀₀)

⇒ $4984 = P (^{100 + 12}/₁₀₀)

⇒ $4984 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4984

⇒ P = ⁴⁹⁸⁴/_¹¹²/100

⇒ P = 4984 × ¹⁰⁰/₁₁₂

⇒ P = ^{4984 × 100}/₁₁₂

⇒ P = ⁴⁹⁸⁴⁰⁰/₁₁₂

⇒ P = $4450

Thus, the sum borrowed (P) = $4450 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 12

Thus, simple interest for 3 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 4984, then the Principal = ¹⁰⁰/₁₁₂ × 4984

= ^{100 × 4984}/₁₁₂

= ⁴⁹⁸⁴⁰⁰/₁₁₂

= 4450

Thus, Principal = $4450

Thus, the sum borrowed = $4450 Answer

Similar Questions

(1) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 8 years.

(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 7 years.

(3) How much loan did Karen borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7140 to clear it?

(4) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.

(5) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7216 to clear the loan, then find the time period of the loan.

(6) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?

(7) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.

(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 8 years.

(9) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 8 years.