Simple Interest
Math MCQs

Question :    Nancy had to pay $4648 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  $4150

Solution & Explanation

Solution

Given,

Amount (A) = $4648

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

$4648 = P (1 + 4% × 3)

⇒ $4648 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4648 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $4648 = P (1 + ¹²/₁₀₀)

⇒ $4648 = P (^{100 + 12}/₁₀₀)

⇒ $4648 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4648

⇒ P = ⁴⁶⁴⁸/_¹¹²/100

⇒ P = 4648 × ¹⁰⁰/₁₁₂

⇒ P = ^{4648 × 100}/₁₁₂

⇒ P = ⁴⁶⁴⁸⁰⁰/₁₁₂

⇒ P = $4150

Thus, the sum borrowed (P) = $4150 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 4648, then the Principal = ¹⁰⁰/₁₁₂ × 4648

= ^{100 × 4648}/₁₁₂

= ⁴⁶⁴⁸⁰⁰/₁₁₂

= 4150

Thus, Principal = $4150

Thus, the sum borrowed = $4150 Answer

Similar Questions

(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 8 years.

(2) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.

(3) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 9% simple interest.

(4) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 3% simple interest?

(5) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.

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

(7) How much loan did David borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6750 to clear it?

(8) Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 3 years.

(9) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 10% simple interest?

(10) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.