Simple Interest
Math MCQs

Question :    Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5100

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $10200

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $10200 – $5100 = $5100

Thus, Simple Interest = $5100

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 5100}/_{5100 × 10}

= ⁵¹⁰⁰⁰⁰/₅₁₀₀₀

= 10 years (using formula)

Thus, Time (T) = 10 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $5100

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $5100 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 10% of Principal

= 10% of $5100

= ¹⁰/₁₀₀ × 5100

= ^{10 × 5100}/₁₀₀

= ⁵¹⁰⁰⁰/₁₀₀ = 510

Thus, simple Interest for 1 year = $510

Now,

∵ If the simple Interest is $510, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₁₀ years

∴ If the simple Interest is $5100, then the time = ¹/₅₁₀ × 5100 years

= ^{1 × 5100}/₅₁₀ years

= ⁵¹⁰⁰/₅₁₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 8 years.

(2) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?

(3) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.

(4) How much loan did Laura borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9812.5 to clear it?

(5) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.

(6) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 3% simple interest?

(7) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9348 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 3 years.

(9) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.

(10) Patricia had to pay $3528 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.