Simple Interest
Math MCQs

Question :  ( 1 of 10 )  William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5000

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

Amount (A) = $8000

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 = $8000 – $5000 = $3000

Thus, Simple Interest = $3000

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 × 3000}/_{5000 × 10}

= ³⁰⁰⁰⁰⁰/₅₀₀₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $5000

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

Simple Interest = $3000 (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 $5000

= ¹⁰/₁₀₀ × 5000

= ^{10 × 5000}/₁₀₀

= ⁵⁰⁰⁰⁰/₁₀₀ = 500

Thus, simple Interest for 1 year = $500

Now,

∵ If the simple Interest is $500, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₀₀ years

∴ If the simple Interest is $3000, then the time = ¹/₅₀₀ × 3000 years

= ^{1 × 3000}/₅₀₀ years

= ³⁰⁰⁰/₅₀₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 3 years.

(2) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 9% simple interest?

(3) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(4) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.

(6) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 8 years.

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

(9) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 4 years.

(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 8 years.