Simple Interest
Math MCQs

Question :    Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9512 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5800

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

Amount (A) = $9512

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 = $9512 – $5800 = $3712

Thus, Simple Interest = $3712

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 × 3712}/_{5800 × 8}

= ³⁷¹²⁰⁰/₄₆₄₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $5800

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

Simple Interest = $3712 (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 $5800

= ⁸/₁₀₀ × 5800

= ^{8 × 5800}/₁₀₀

= ⁴⁶⁴⁰⁰/₁₀₀ = 464

Thus, simple Interest for 1 year = $464

Now,

∵ If the simple Interest is $464, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₆₄ years

∴ If the simple Interest is $3712, then the time = ¹/₄₆₄ × 3712 years

= ^{1 × 3712}/₄₆₄ years

= ³⁷¹²/₄₆₄ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7003 to clear the loan, then find the time period of the loan.

(2) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.

(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 3 years.

(5) In how much time a principal of $3000 will amount to $3600 at a simple interest of 4% per annum?

(6) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.

(7) What amount does William have to pay after 5 years if he takes a loan of $3500 at 5% simple interest?

(8) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.

(9) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.

(10) What amount does William have to pay after 6 years if he takes a loan of $3500 at 4% simple interest?