Simple Interest
Math MCQs

Question :    Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4600

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $7176

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 = $7176 – $4600 = $2576

Thus, Simple Interest = $2576

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 × 2576}/_{4600 × 8}

= ²⁵⁷⁶⁰⁰/₃₆₈₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = $4600

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $2576 (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 = 8% of Principal

= 8% of $4600

= ⁸/₁₀₀ × 4600

= ^{8 × 4600}/₁₀₀

= ³⁶⁸⁰⁰/₁₀₀ = 368

Thus, simple Interest for 1 year = $368

Now,

∵ If the simple Interest is $368, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₆₈ years

∴ If the simple Interest is $2576, then the time = ¹/₃₆₈ × 2576 years

= ^{1 × 2576}/₃₆₈ years

= ²⁵⁷⁶/₃₆₈ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.

(2) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.

(4) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.

(6) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 10% simple interest?

(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 8 years.

(8) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.

(9) In how much time a principal of $3050 will amount to $3812.5 at a simple interest of 5% per annum?

(10) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.