Simple Interest
Math MCQs

Question :    Andrew had to pay $5520 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

Correct Answer  $4800

Solution & Explanation

Solution

Given,

Amount (A) = $5520

Rate of Simple Interest (R) = 5%

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

$5520 = P (1 + 5% × 3)

⇒ $5520 = P (1 + ⁵/₁₀₀ × 3)

⇒ $5520 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $5520 = P (1 + ¹⁵/₁₀₀)

⇒ $5520 = P (^{100 + 15}/₁₀₀)

⇒ $5520 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5520

⇒ P = ⁵⁵²⁰/_¹¹⁵/100

⇒ P = 5520 × ¹⁰⁰/₁₁₅

⇒ P = ^{5520 × 100}/₁₁₅

⇒ P = ⁵⁵²⁰⁰⁰/₁₁₅

⇒ P = $4800

Thus, the sum borrowed (P) = $4800 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 15

Thus, simple interest for 3 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 5520, then the Principal = ¹⁰⁰/₁₁₅ × 5520

= ^{100 × 5520}/₁₁₅

= ⁵⁵²⁰⁰⁰/₁₁₅

= 4800

Thus, Principal = $4800

Thus, the sum borrowed = $4800 Answer

Similar Questions

(1) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.

(2) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?

(3) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 4% simple interest?

(4) If Mary borrowed $3050 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(5) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 4% simple interest?

(6) How much loan did Joseph borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6270 to clear it?

(7) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 7% simple interest?

(8) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 3 years.

(9) 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.

(10) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 8% simple interest?