Simple Interest
Math MCQs

Question :    Kenneth had to pay $5600 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  $5000

Solution & Explanation

Solution

Given,

Amount (A) = $5600

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

$5600 = P (1 + 4% × 3)

⇒ $5600 = P (1 + ⁴/₁₀₀ × 3)

⇒ $5600 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $5600 = P (1 + ¹²/₁₀₀)

⇒ $5600 = P (^{100 + 12}/₁₀₀)

⇒ $5600 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5600

⇒ P = ⁵⁶⁰⁰/_¹¹²/100

⇒ P = 5600 × ¹⁰⁰/₁₁₂

⇒ P = ^{5600 × 100}/₁₁₂

⇒ P = ⁵⁶⁰⁰⁰⁰/₁₁₂

⇒ P = $5000

Thus, the sum borrowed (P) = $5000 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 5600, then the Principal = ¹⁰⁰/₁₁₂ × 5600

= ^{100 × 5600}/₁₁₂

= ⁵⁶⁰⁰⁰⁰/₁₁₂

= 5000

Thus, Principal = $5000

Thus, the sum borrowed = $5000 Answer

Similar Questions

(1) Mary had to pay $3324.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(2) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 3 years.

(3) Michelle had to pay $5247 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 8 years.

(5) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 2% simple interest?

(6) Patricia had to pay $3622.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 9% simple interest.

(8) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.

(9) Emily had to pay $5320 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

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