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 $8313 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5100

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $8313

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 = $8313 – $5100 = $3213

Thus, Simple Interest = $3213

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 × 3213}/_{5100 × 7}

= ³²¹³⁰⁰/₃₅₇₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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 = $3213 (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 $3213, then the time = ¹/₃₅₇ × 3213 years

= ^{1 × 3213}/₃₅₇ years

= ³²¹³/₃₅₇ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) What amount does John have to pay after 5 years if he takes a loan of $3200 at 5% simple interest?

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

(3) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.

(4) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(5) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.

(6) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.

(7) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.

(8) How much loan did Jacob borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8800 to clear it?

(9) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 4% simple interest.

(10) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 4 years.