Simple Interest
Math MCQs

Question :    William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5000

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

Amount (A) = $7100

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 = $7100 – $5000 = $2100

Thus, Simple Interest = $2100

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 × 2100}/_{5000 × 7}

= ²¹⁰⁰⁰⁰/₃₅₀₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = 7% per annum

Simple Interest = $2100 (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 $5000

= ⁷/₁₀₀ × 5000

= ^{7 × 5000}/₁₀₀

= ³⁵⁰⁰⁰/₁₀₀ = 350

Thus, simple Interest for 1 year = $350

Now,

∵ If the simple Interest is $350, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₅₀ years

∴ If the simple Interest is $2100, then the time = ¹/₃₅₀ × 2100 years

= ^{1 × 2100}/₃₅₀ years

= ²¹⁰⁰/₃₅₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 3 years.

(2) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.

(3) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 8% simple interest?

(4) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.

(5) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 3% simple interest?

(6) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.

(7) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 4% simple interest?

(8) If Charles paid $4680 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 Michael borrowed a sum of $3150 at a 6% simple interest?

(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 3 years.