Simple Interest
Math MCQs

Question :    How much loan did Jessica borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7187.5 to clear it?

Correct Answer  $5750

Solution & Explanation

Solution

Given,

Amount (A) = $7187.5

Rate of Simple Interest (R) = 5%

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

$7187.5 = P (1 + 5% × 5)

⇒ $7187.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7187.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7187.5 = P (1 + ²⁵/₁₀₀)

⇒ $7187.5 = P (^{100 + 25}/₁₀₀)

⇒ $7187.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7187.5

⇒ P = ^7187.5/_¹²⁵/100

⇒ P = 7187.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{7187.5 × 100}/₁₂₅

⇒ P = ⁷¹⁸⁷⁵⁰/₁₂₅

⇒ 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 = 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 = 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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 7187.5, then the Principal = ¹⁰⁰/₁₂₅ × 7187.5

= ^{100 × 7187.5}/₁₂₅

= ⁷¹⁸⁷⁵⁰/₁₂₅

= 5750

Thus, Principal = $5750

Thus, the sum borrowed = $5750 Answer

Similar Questions

(1) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 3% simple interest.

(3) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 4% simple interest?

(4) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.

(5) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 10% simple interest?

(6) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7616 to clear the loan, then find the time period of the loan.

(7) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.

(8) How much loan did David borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6750 to clear it?

(9) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 4 years.

(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 7 years.