Simple Interest
Math MCQs

Question :    If Donna paid $5626 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4850

Solution & Explanation

Solution

Given,

Amount (A) = $5626

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

$5626 = P (1 + 4% × 4)

⇒ $5626 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5626 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5626 = P (1 + ¹⁶/₁₀₀)

⇒ $5626 = P (^{100 + 16}/₁₀₀)

⇒ $5626 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5626

⇒ P = ⁵⁶²⁶/_¹¹⁶/100

⇒ P = 5626 × ¹⁰⁰/₁₁₆

⇒ P = ^{5626 × 100}/₁₁₆

⇒ P = ⁵⁶²⁶⁰⁰/₁₁₆

⇒ P = $4850

Thus, the sum borrowed (P) = $4850 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 5626, then the Principal = ¹⁰⁰/₁₁₆ × 5626

= ^{100 × 5626}/₁₁₆

= ⁵⁶²⁶⁰⁰/₁₁₆

= 4850

Thus, Principal = $4850

Thus, the sum borrowed = $4850 Answer

Similar Questions

(1) If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 4 years.

(3) What amount does William have to pay after 5 years if he takes a loan of $3500 at 7% simple interest?

(4) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 3 years.

(6) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 7 years.

(7) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.

(8) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.

(9) If Karen borrowed $3950 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(10) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 4% simple interest.