Simple Interest
Math MCQs

Question :    Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10860 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6000

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $10860

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 = $10860 – $6000 = $4860

Thus, Simple Interest = $4860

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 × 4860}/_{6000 × 9}

= ⁴⁸⁶⁰⁰⁰/₅₄₀₀₀

= 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) = $6000

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $4860 (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 = 9% of Principal

= 9% of $6000

= ⁹/₁₀₀ × 6000

= ^{9 × 6000}/₁₀₀

= ⁵⁴⁰⁰⁰/₁₀₀ = 540

Thus, simple Interest for 1 year = $540

Now,

∵ If the simple Interest is $540, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₄₀ years

∴ If the simple Interest is $4860, then the time = ¹/₅₄₀ × 4860 years

= ^{1 × 4860}/₅₄₀ years

= ⁴⁸⁶⁰/₅₄₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 10% simple interest.

(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 8 years.

(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.

(4) How much loan did Edward borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9120 to clear it?

(5) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?

(6) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.

(7) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.

(8) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7208 to clear the loan, then find the time period of the loan.

(9) If Sarah borrowed $3850 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(10) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?