Simple Interest
Math MCQs

Question :    Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4700

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $8460

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 = $8460 – $4700 = $3760

Thus, Simple Interest = $3760

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 × 3760}/_{4700 × 10}

= ³⁷⁶⁰⁰⁰/₄₇₀₀₀

= 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) = $4700

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $3760 (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 = 10% of Principal

= 10% of $4700

= ¹⁰/₁₀₀ × 4700

= ^{10 × 4700}/₁₀₀

= ⁴⁷⁰⁰⁰/₁₀₀ = 470

Thus, simple Interest for 1 year = $470

Now,

∵ If the simple Interest is $470, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₇₀ years

∴ If the simple Interest is $3760, then the time = ¹/₄₇₀ × 3760 years

= ^{1 × 3760}/₄₇₀ years

= ³⁷⁶⁰/₄₇₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 3 years.

(3) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 3 years.

(4) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 7% simple interest?

(5) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 2% simple interest.

(6) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 5% simple interest?

(7) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 4 years.

(9) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.

(10) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 6% simple interest?