Simple Interest
Math MCQs

Question :    How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?

Correct Answer  $7450

Solution & Explanation

Solution

Given,

Amount (A) = $9312.5

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

$9312.5 = P (1 + 5% × 5)

⇒ $9312.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9312.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9312.5 = P (1 + ²⁵/₁₀₀)

⇒ $9312.5 = P (^{100 + 25}/₁₀₀)

⇒ $9312.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9312.5

⇒ P = ^9312.5/_¹²⁵/100

⇒ P = 9312.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{9312.5 × 100}/₁₂₅

⇒ P = ⁹³¹²⁵⁰/₁₂₅

⇒ P = $7450

Thus, the sum borrowed (P) = $7450 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 9312.5, then the Principal = ¹⁰⁰/₁₂₅ × 9312.5

= ^{100 × 9312.5}/₁₂₅

= ⁹³¹²⁵⁰/₁₂₅

= 7450

Thus, Principal = $7450

Thus, the sum borrowed = $7450 Answer

Similar Questions

(1) What amount does James have to pay after 6 years if he takes a loan of $3000 at 6% simple interest?

(2) Anthony had to pay $4945 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 8 years.

(4) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 4 years.

(5) If Donna paid $5626 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?

(7) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.

(8) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 5% simple interest?

(9) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.

(10) How much loan did Paul borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8040 to clear it?