Simple Interest
Math MCQs

Question :    William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5000

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

Amount (A) = $8000

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 = $8000 – $5000 = $3000

Thus, Simple Interest = $3000

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 × 3000}/_{5000 × 6}

= ³⁰⁰⁰⁰⁰/₃₀₀₀₀

= 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) = $5000

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

Simple Interest = $3000 (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 $5000

= ⁶/₁₀₀ × 5000

= ^{6 × 5000}/₁₀₀

= ³⁰⁰⁰⁰/₁₀₀ = 300

Thus, simple Interest for 1 year = $300

Now,

∵ If the simple Interest is $300, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₀₀ years

∴ If the simple Interest is $3000, then the time = ¹/₃₀₀ × 3000 years

= ^{1 × 3000}/₃₀₀ years

= ³⁰⁰⁰/₃₀₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8312.5 to clear it?

(2) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 4% simple interest?

(3) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.

(4) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.

(5) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 4 years.

(6) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 9% simple interest?

(7) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.

(8) If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 5% simple interest?

(10) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 2% simple interest?