Simple Interest
Math MCQs

Question :    If Christopher paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4000

Solution & Explanation

Solution

Given,

Amount (A) = $4320

Rate of Simple Interest (R) = 2%

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

$4320 = P (1 + 2% × 4)

⇒ $4320 = P (1 + ²/₁₀₀ × 4)

⇒ $4320 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4320 = P (1 + ⁸/₁₀₀)

⇒ $4320 = P (^{100 + 8}/₁₀₀)

⇒ $4320 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4320

⇒ P = ⁴³²⁰/_¹⁰⁸/100

⇒ P = 4320 × ¹⁰⁰/₁₀₈

⇒ P = ^{4320 × 100}/₁₀₈

⇒ P = ⁴³²⁰⁰⁰/₁₀₈

⇒ P = $4000

Thus, the sum borrowed (P) = $4000 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 4320, then the Principal = ¹⁰⁰/₁₀₈ × 4320

= ^{100 × 4320}/₁₀₈

= ⁴³²⁰⁰⁰/₁₀₈

= 4000

Thus, Principal = $4000

Thus, the sum borrowed = $4000 Answer

Similar Questions

(1) How much loan did Laura borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9420 to clear it?

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

(3) If Kimberly paid $5394 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(4) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.

(5) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.

(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 7 years.

(7) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 6% simple interest?

(8) What amount does James have to pay after 5 years if he takes a loan of $3000 at 2% simple interest?

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

(10) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.