Simple Interest
Math MCQs

Question :    Steven had to pay $5290 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  $4600

Solution & Explanation

Solution

Given,

Amount (A) = $5290

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

$5290 = P (1 + 5% × 3)

⇒ $5290 = P (1 + ⁵/₁₀₀ × 3)

⇒ $5290 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $5290 = P (1 + ¹⁵/₁₀₀)

⇒ $5290 = P (^{100 + 15}/₁₀₀)

⇒ $5290 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5290

⇒ P = ⁵²⁹⁰/_¹¹⁵/100

⇒ P = 5290 × ¹⁰⁰/₁₁₅

⇒ P = ^{5290 × 100}/₁₁₅

⇒ P = ⁵²⁹⁰⁰⁰/₁₁₅

⇒ P = $4600

Thus, the sum borrowed (P) = $4600 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 5290, then the Principal = ¹⁰⁰/₁₁₅ × 5290

= ^{100 × 5290}/₁₁₅

= ⁵²⁹⁰⁰⁰/₁₁₅

= 4600

Thus, Principal = $4600

Thus, the sum borrowed = $4600 Answer

Similar Questions

(1) How much loan did Carol borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7755 to clear it?

(2) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 3 years.

(3) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.

(4) If Donna paid $5432 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) How much loan did Paul borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8375 to clear it?

(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 8 years.

(7) If Anthony paid $4644 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?

(9) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?

(10) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.