Simple Interest
Math MCQs

Question :    How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?

Correct Answer  $7800

Solution & Explanation

Solution

Given,

Amount (A) = $9750

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

$9750 = P (1 + 5% × 5)

⇒ $9750 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9750 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9750 = P (1 + ²⁵/₁₀₀)

⇒ $9750 = P (^{100 + 25}/₁₀₀)

⇒ $9750 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9750

⇒ P = ⁹⁷⁵⁰/_¹²⁵/100

⇒ P = 9750 × ¹⁰⁰/₁₂₅

⇒ P = ^{9750 × 100}/₁₂₅

⇒ P = ⁹⁷⁵⁰⁰⁰/₁₂₅

⇒ P = $7800

Thus, the sum borrowed (P) = $7800 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 9750, then the Principal = ¹⁰⁰/₁₂₅ × 9750

= ^{100 × 9750}/₁₂₅

= ⁹⁷⁵⁰⁰⁰/₁₂₅

= 7800

Thus, Principal = $7800

Thus, the sum borrowed = $7800 Answer

Similar Questions

(1) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 5% simple interest?

(2) How much loan did Sharon borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9300 to clear it?

(3) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.

(4) How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?

(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 3 years.

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

(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.

(8) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 4 years.

(10) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 5% simple interest?