Simple Interest
Math MCQs

Question :    If Elizabeth paid $3726 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3450

Solution & Explanation

Solution

Given,

Amount (A) = $3726

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

$3726 = P (1 + 2% × 4)

⇒ $3726 = P (1 + ²/₁₀₀ × 4)

⇒ $3726 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3726 = P (1 + ⁸/₁₀₀)

⇒ $3726 = P (^{100 + 8}/₁₀₀)

⇒ $3726 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3726

⇒ P = ³⁷²⁶/_¹⁰⁸/100

⇒ P = 3726 × ¹⁰⁰/₁₀₈

⇒ P = ^{3726 × 100}/₁₀₈

⇒ P = ³⁷²⁶⁰⁰/₁₀₈

⇒ P = $3450

Thus, the sum borrowed (P) = $3450 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 3726, then the Principal = ¹⁰⁰/₁₀₈ × 3726

= ^{100 × 3726}/₁₀₈

= ³⁷²⁶⁰⁰/₁₀₈

= 3450

Thus, Principal = $3450

Thus, the sum borrowed = $3450 Answer

Similar Questions

(1) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 3 years.

(2) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 3 years.

(3) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 8% simple interest?

(4) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.

(5) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.

(6) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.

(7) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 6% simple interest?

(8) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 7 years.

(9) How much loan did Andrew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7820 to clear it?

(10) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?