Simple Interest
Math MCQs

Question :    Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8670 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) = 7% per annum

Amount (A) = $8670

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 = $8670 – $5100 = $3570

Thus, Simple Interest = $3570

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 × 3570}/_{5100 × 7}

= ³⁵⁷⁰⁰⁰/₃₅₇₀₀

= 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) = 7% per annum

Simple Interest = $3570 (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 = 7% of Principal

= 7% of $5100

= ⁷/₁₀₀ × 5100

= ^{7 × 5100}/₁₀₀

= ³⁵⁷⁰⁰/₁₀₀ = 357

Thus, simple Interest for 1 year = $357

Now,

∵ If the simple Interest is $357, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₅₇ years

∴ If the simple Interest is $3570, then the time = ¹/₃₅₇ × 3570 years

= ^{1 × 3570}/₃₅₇ years

= ³⁵⁷⁰/₃₅₇ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 3 years.

(2) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.

(3) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $9200 to clear the loan, then find the time period of the loan.

(4) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 4 years.

(6) In how much time a principal of $3150 will amount to $3276 at a simple interest of 2% per annum?

(7) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 4 years.

(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 7 years.

(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 8 years.

(10) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.