Simple Interest
Math MCQs

Question :    If Linda paid $3752 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3350

Solution & Explanation

Solution

Given,

Amount (A) = $3752

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

$3752 = P (1 + 3% × 4)

⇒ $3752 = P (1 + ³/₁₀₀ × 4)

⇒ $3752 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $3752 = P (1 + ¹²/₁₀₀)

⇒ $3752 = P (^{100 + 12}/₁₀₀)

⇒ $3752 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3752

⇒ P = ³⁷⁵²/_¹¹²/100

⇒ P = 3752 × ¹⁰⁰/₁₁₂

⇒ P = ^{3752 × 100}/₁₁₂

⇒ P = ³⁷⁵²⁰⁰/₁₁₂

⇒ P = $3350

Thus, the sum borrowed (P) = $3350 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 3752, then the Principal = ¹⁰⁰/₁₁₂ × 3752

= ^{100 × 3752}/₁₁₂

= ³⁷⁵²⁰⁰/₁₁₂

= 3350

Thus, Principal = $3350

Thus, the sum borrowed = $3350 Answer

Similar Questions

(1) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 4% simple interest?

(2) How much loan did George borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8760 to clear it?

(3) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 3 years.

(5) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $13000 to clear the loan, then find the time period of the loan.

(6) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 7 years.

(8) How much loan did Andrew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8160 to clear it?

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

(10) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.