Simple Interest
Math MCQs

Question :    How much loan did Amanda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8222.5 to clear it?

Correct Answer  $7150

Solution & Explanation

Solution

Given,

Amount (A) = $8222.5

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

$8222.5 = P (1 + 3% × 5)

⇒ $8222.5 = P (1 + ³/₁₀₀ × 5)

⇒ $8222.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8222.5 = P (1 + ¹⁵/₁₀₀)

⇒ $8222.5 = P (^{100 + 15}/₁₀₀)

⇒ $8222.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8222.5

⇒ P = ^8222.5/_¹¹⁵/100

⇒ P = 8222.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{8222.5 × 100}/₁₁₅

⇒ P = ⁸²²²⁵⁰/₁₁₅

⇒ P = $7150

Thus, the sum borrowed (P) = $7150 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 8222.5, then the Principal = ¹⁰⁰/₁₁₅ × 8222.5

= ^{100 × 8222.5}/₁₁₅

= ⁸²²²⁵⁰/₁₁₅

= 7150

Thus, Principal = $7150

Thus, the sum borrowed = $7150 Answer

Similar Questions

(1) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 9% simple interest?

(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.

(3) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 4% simple interest?

(4) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 5% simple interest?

(5) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8364 to clear the loan, then find the time period of the loan.

(6) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.

(7) 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.

(8) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 10% simple interest?

(9) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.

(10) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 4% simple interest?