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) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 2% simple interest?

(2) 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.

(3) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 7 years.

(4) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9238 to clear the loan, then find the time period of the loan.

(5) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 7% simple interest.

(7) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.

(8) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(9) Ashley had to pay $5232.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 7 years.