Simple Interest
Math MCQs

Question :    If Emily paid $5320 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4750

Solution & Explanation

Solution

Given,

Amount (A) = $5320

Rate of Simple Interest (R) = 3%

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

$5320 = P (1 + 3% × 4)

⇒ $5320 = P (1 + ³/₁₀₀ × 4)

⇒ $5320 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $5320 = P (1 + ¹²/₁₀₀)

⇒ $5320 = P (^{100 + 12}/₁₀₀)

⇒ $5320 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5320

⇒ P = ⁵³²⁰/_¹¹²/100

⇒ P = 5320 × ¹⁰⁰/₁₁₂

⇒ P = ^{5320 × 100}/₁₁₂

⇒ P = ⁵³²⁰⁰⁰/₁₁₂

⇒ P = $4750

Thus, the sum borrowed (P) = $4750 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 12

Thus, simple interest for 4 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 5320, then the Principal = ¹⁰⁰/₁₁₂ × 5320

= ^{100 × 5320}/₁₁₂

= ⁵³²⁰⁰⁰/₁₁₂

= 4750

Thus, Principal = $4750

Thus, the sum borrowed = $4750 Answer

Similar Questions

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

(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 3 years.

(3) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 7% simple interest?

(4) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?

(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 4 years.

(6) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.

(8) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 8 years.

(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 8 years.

(10) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.