Simple Interest
Math MCQs

Question :    If Elizabeth paid $4002 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3450

Solution & Explanation

Solution

Given,

Amount (A) = $4002

Rate of Simple Interest (R) = 4%

Time (T) = 4 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

$4002 = P (1 + 4% × 4)

⇒ $4002 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4002 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4002 = P (1 + ¹⁶/₁₀₀)

⇒ $4002 = P (^{100 + 16}/₁₀₀)

⇒ $4002 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4002

⇒ P = ⁴⁰⁰²/_¹¹⁶/100

⇒ P = 4002 × ¹⁰⁰/₁₁₆

⇒ P = ^{4002 × 100}/₁₁₆

⇒ P = ⁴⁰⁰²⁰⁰/₁₁₆

⇒ P = $3450

Thus, the sum borrowed (P) = $3450 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 = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 4002, then the Principal = ¹⁰⁰/₁₁₆ × 4002

= ^{100 × 4002}/₁₁₆

= ⁴⁰⁰²⁰⁰/₁₁₆

= 3450

Thus, Principal = $3450

Thus, the sum borrowed = $3450 Answer

Similar Questions

(1) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 4 years.

(2) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.

(3) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 7% simple interest.

(4) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 7 years.

(6) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 4 years.

(7) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 6% simple interest?

(8) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 4 years.

(10) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.