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 Robert borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6120 to clear it?

(2) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 7 years.

(3) 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.

(4) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.

(5) If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.

(7) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.

(9) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 9% simple interest?

(10) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 8% simple interest?