Simple Interest
Math MCQs

Question :    If Sandra paid $4806 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4450

Solution & Explanation

Solution

Given,

Amount (A) = $4806

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

$4806 = P (1 + 2% × 4)

⇒ $4806 = P (1 + ²/₁₀₀ × 4)

⇒ $4806 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4806 = P (1 + ⁸/₁₀₀)

⇒ $4806 = P (^{100 + 8}/₁₀₀)

⇒ $4806 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4806

⇒ P = ⁴⁸⁰⁶/_¹⁰⁸/100

⇒ P = 4806 × ¹⁰⁰/₁₀₈

⇒ P = ^{4806 × 100}/₁₀₈

⇒ P = ⁴⁸⁰⁶⁰⁰/₁₀₈

⇒ P = $4450

Thus, the sum borrowed (P) = $4450 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 4806, then the Principal = ¹⁰⁰/₁₀₈ × 4806

= ^{100 × 4806}/₁₀₈

= ⁴⁸⁰⁶⁰⁰/₁₀₈

= 4450

Thus, Principal = $4450

Thus, the sum borrowed = $4450 Answer

Similar Questions

(1) How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?

(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 7 years.

(3) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.

(4) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 9% simple interest?

(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 4 years.

(6) In how much time a principal of $3150 will amount to $3402 at a simple interest of 2% per annum?

(7) In how much time a principal of $3100 will amount to $3596 at a simple interest of 4% per annum?

(8) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 7 years.

(9) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6258 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 7 years.