Simple Interest
Math MCQs

Question :    Paul had to pay $5264 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  $4700

Solution & Explanation

Solution

Given,

Amount (A) = $5264

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

$5264 = P (1 + 4% × 3)

⇒ $5264 = P (1 + ⁴/₁₀₀ × 3)

⇒ $5264 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $5264 = P (1 + ¹²/₁₀₀)

⇒ $5264 = P (^{100 + 12}/₁₀₀)

⇒ $5264 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5264

⇒ P = ⁵²⁶⁴/_¹¹²/100

⇒ P = 5264 × ¹⁰⁰/₁₁₂

⇒ P = ^{5264 × 100}/₁₁₂

⇒ P = ⁵²⁶⁴⁰⁰/₁₁₂

⇒ P = $4700

Thus, the sum borrowed (P) = $4700 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 5264, then the Principal = ¹⁰⁰/₁₁₂ × 5264

= ^{100 × 5264}/₁₁₂

= ⁵²⁶⁴⁰⁰/₁₁₂

= 4700

Thus, Principal = $4700

Thus, the sum borrowed = $4700 Answer

Similar Questions

(1) How much loan did Nancy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6765 to clear it?

(2) What amount does John have to pay after 5 years if he takes a loan of $3200 at 6% simple interest?

(3) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.

(4) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 7% simple interest?

(5) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 3% simple interest?

(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 7 years.

(7) How much loan did Patricia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5922.5 to clear it?

(8) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.

(9) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.