Simple Interest
Math MCQs

Question :    Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4700

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

Amount (A) = $7661

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 = $7661 – $4700 = $2961

Thus, Simple Interest = $2961

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 × 2961}/_{4700 × 7}

= ²⁹⁶¹⁰⁰/₃₂₉₀₀

= 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) = $4700

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

Simple Interest = $2961 (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 $4700

= ⁷/₁₀₀ × 4700

= ^{7 × 4700}/₁₀₀

= ³²⁹⁰⁰/₁₀₀ = 329

Thus, simple Interest for 1 year = $329

Now,

∵ If the simple Interest is $329, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₂₉ years

∴ If the simple Interest is $2961, then the time = ¹/₃₂₉ × 2961 years

= ^{1 × 2961}/₃₂₉ years

= ²⁹⁶¹/₃₂₉ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.

(2) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.

(3) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.

(4) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 10% simple interest?

(6) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $5848 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.

(8) What amount will be due after 2 years if William borrowed a sum of $3250 at a 5% simple interest?

(9) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 4 years.

(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.