Simple Interest
Math MCQs

Question :    If Daniel paid $4592 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4100

Solution & Explanation

Solution

Given,

Amount (A) = $4592

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

$4592 = P (1 + 3% × 4)

⇒ $4592 = P (1 + ³/₁₀₀ × 4)

⇒ $4592 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4592 = P (1 + ¹²/₁₀₀)

⇒ $4592 = P (^{100 + 12}/₁₀₀)

⇒ $4592 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4592

⇒ P = ⁴⁵⁹²/_¹¹²/100

⇒ P = 4592 × ¹⁰⁰/₁₁₂

⇒ P = ^{4592 × 100}/₁₁₂

⇒ P = ⁴⁵⁹²⁰⁰/₁₁₂

⇒ P = $4100

Thus, the sum borrowed (P) = $4100 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 4592, then the Principal = ¹⁰⁰/₁₁₂ × 4592

= ^{100 × 4592}/₁₁₂

= ⁴⁵⁹²⁰⁰/₁₁₂

= 4100

Thus, Principal = $4100

Thus, the sum borrowed = $4100 Answer

Similar Questions

(1) How much loan did Daniel borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7320 to clear it?

(2) Elizabeth had to pay $3967.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 9% simple interest?

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

(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.

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

(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 7 years.

(8) Margaret had to pay $5002.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(9) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.

(10) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?