Simple Interest
Math MCQs

Question :    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.

Correct Answer  $4750

Solution & Explanation

Solution

Given,

Amount (A) = $5320

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

$5320 = P (1 + 4% × 3)

⇒ $5320 = P (1 + ⁴/₁₀₀ × 3)

⇒ $5320 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $5320 = P (1 + ¹²/₁₀₀)

⇒ $5320 = P (^{100 + 12}/₁₀₀)

⇒ $5320 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5320

⇒ P = ⁵³²⁰/_¹¹²/100

⇒ P = 5320 × ¹⁰⁰/₁₁₂

⇒ P = ^{5320 × 100}/₁₁₂

⇒ P = ⁵³²⁰⁰⁰/₁₁₂

⇒ P = $4750

Thus, the sum borrowed (P) = $4750 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 5320, then the Principal = ¹⁰⁰/₁₁₂ × 5320

= ^{100 × 5320}/₁₁₂

= ⁵³²⁰⁰⁰/₁₁₂

= 4750

Thus, Principal = $4750

Thus, the sum borrowed = $4750 Answer

Similar Questions

(1) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?

(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 8 years.

(3) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 4% simple interest?

(5) 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.

(6) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 7 years.

(8) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 10% simple interest?

(9) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 8% simple interest?

(10) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 4 years.