Simple Interest
Math MCQs

Question :    Lisa had to pay $4536 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $4050

Solution & Explanation

Solution

Given,

Amount (A) = $4536

Rate of Simple Interest (R) = 4%

Time (T) = 3 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

$4536 = P (1 + 4% × 3)

⇒ $4536 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4536 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $4536 = P (1 + ¹²/₁₀₀)

⇒ $4536 = P (^{100 + 12}/₁₀₀)

⇒ $4536 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4536

⇒ P = ⁴⁵³⁶/_¹¹²/100

⇒ P = 4536 × ¹⁰⁰/₁₁₂

⇒ P = ^{4536 × 100}/₁₁₂

⇒ P = ⁴⁵³⁶⁰⁰/₁₁₂

⇒ P = $4050

Thus, the sum borrowed (P) = $4050 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

Calculation of the Amount

Since, in the question, time = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 4 = 12

Thus, simple interest for 3 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 4536, then the Principal = ¹⁰⁰/₁₁₂ × 4536

= ^{100 × 4536}/₁₁₂

= ⁴⁵³⁶⁰⁰/₁₁₂

= 4050

Thus, Principal = $4050

Thus, the sum borrowed = $4050 Answer

Similar Questions

(1) If Susan paid $4234 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(2) How much loan did Susan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6215 to clear it?

(3) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.

(4) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 8% simple interest?

(6) If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 3 years.

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

(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.

(10) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 6% simple interest?