Simple Interest
Math MCQs

Question :    How much loan did Ryan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9875 to clear it?

Correct Answer  $7900

Solution & Explanation

Solution

Given,

Amount (A) = $9875

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

$9875 = P (1 + 5% × 5)

⇒ $9875 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9875 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9875 = P (1 + ²⁵/₁₀₀)

⇒ $9875 = P (^{100 + 25}/₁₀₀)

⇒ $9875 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9875

⇒ P = ⁹⁸⁷⁵/_¹²⁵/100

⇒ P = 9875 × ¹⁰⁰/₁₂₅

⇒ P = ^{9875 × 100}/₁₂₅

⇒ P = ⁹⁸⁷⁵⁰⁰/₁₂₅

⇒ P = $7900

Thus, the sum borrowed (P) = $7900 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 9875, then the Principal = ¹⁰⁰/₁₂₅ × 9875

= ^{100 × 9875}/₁₂₅

= ⁹⁸⁷⁵⁰⁰/₁₂₅

= 7900

Thus, Principal = $7900

Thus, the sum borrowed = $7900 Answer

Similar Questions

(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 8 years.

(2) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?

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

(4) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 4 years.

(5) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?

(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 4 years.

(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 3 years.

(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 7 years.

(9) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 3 years.