Simple Interest
Math MCQs

Question :    Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6100

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $9028

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 = $9028 – $6100 = $2928

Thus, Simple Interest = $2928

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 × 2928}/_{6100 × 6}

= ²⁹²⁸⁰⁰/₃₆₆₀₀

= 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) = $6100

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2928 (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 = 6% of Principal

= 6% of $6100

= ⁶/₁₀₀ × 6100

= ^{6 × 6100}/₁₀₀

= ³⁶⁶⁰⁰/₁₀₀ = 366

Thus, simple Interest for 1 year = $366

Now,

∵ If the simple Interest is $366, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₆₆ years

∴ If the simple Interest is $2928, then the time = ¹/₃₆₆ × 2928 years

= ^{1 × 2928}/₃₆₆ years

= ²⁹²⁸/₃₆₆ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

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

(2) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 7% simple interest?

(3) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.

(4) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8940 to clear the loan, then find the time period of the loan.

(5) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 4 years.

(7) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 9% simple interest?

(8) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.

(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 7 years.

(10) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 3 years.