Simple Interest
Math MCQs

Question :    How much loan did Jessica borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6612.5 to clear it?

Correct Answer  $5750

Solution & Explanation

Solution

Given,

Amount (A) = $6612.5

Rate of Simple Interest (R) = 3%

Time (T) = 5 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

$6612.5 = P (1 + 3% × 5)

⇒ $6612.5 = P (1 + ³/₁₀₀ × 5)

⇒ $6612.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6612.5 = P (1 + ¹⁵/₁₀₀)

⇒ $6612.5 = P (^{100 + 15}/₁₀₀)

⇒ $6612.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6612.5

⇒ P = ^6612.5/_¹¹⁵/100

⇒ P = 6612.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{6612.5 × 100}/₁₁₅

⇒ P = ⁶⁶¹²⁵⁰/₁₁₅

⇒ P = $5750

Thus, the sum borrowed (P) = $5750 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 3 = 15

Thus, simple interest for 5 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 6612.5, then the Principal = ¹⁰⁰/₁₁₅ × 6612.5

= ^{100 × 6612.5}/₁₁₅

= ⁶⁶¹²⁵⁰/₁₁₅

= 5750

Thus, Principal = $5750

Thus, the sum borrowed = $5750 Answer

Similar Questions

(1) If Sandra paid $4984 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.

(3) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.

(4) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.

(6) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.

(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 9 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.

(9) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.

(10) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.