Simple Interest
Math MCQs

Question :    Mary had to pay $3416 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  $3050

Solution & Explanation

Solution

Given,

Amount (A) = $3416

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

$3416 = P (1 + 4% × 3)

⇒ $3416 = P (1 + ⁴/₁₀₀ × 3)

⇒ $3416 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $3416 = P (1 + ¹²/₁₀₀)

⇒ $3416 = P (^{100 + 12}/₁₀₀)

⇒ $3416 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3416

⇒ P = ³⁴¹⁶/_¹¹²/100

⇒ P = 3416 × ¹⁰⁰/₁₁₂

⇒ P = ^{3416 × 100}/₁₁₂

⇒ P = ³⁴¹⁶⁰⁰/₁₁₂

⇒ P = $3050

Thus, the sum borrowed (P) = $3050 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 3416, then the Principal = ¹⁰⁰/₁₁₂ × 3416

= ^{100 × 3416}/₁₁₂

= ³⁴¹⁶⁰⁰/₁₁₂

= 3050

Thus, Principal = $3050

Thus, the sum borrowed = $3050 Answer

Similar Questions

(1) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?

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

(3) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 9% simple interest?

(4) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.

(5) What amount does David have to pay after 5 years if he takes a loan of $3400 at 10% simple interest?

(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 7 years.

(7) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.

(8) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?

(9) Kimberly had to pay $5208 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.