Simple Interest
Math MCQs

Question :    Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6800

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

Amount (A) = $9656

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 = $9656 – $6800 = $2856

Thus, Simple Interest = $2856

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 × 2856}/_{6800 × 7}

= ²⁸⁵⁶⁰⁰/₄₇₆₀₀

= 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) = $6800

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

Simple Interest = $2856 (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 $6800

= ⁷/₁₀₀ × 6800

= ^{7 × 6800}/₁₀₀

= ⁴⁷⁶⁰⁰/₁₀₀ = 476

Thus, simple Interest for 1 year = $476

Now,

∵ If the simple Interest is $476, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₇₆ years

∴ If the simple Interest is $2856, then the time = ¹/₄₇₆ × 2856 years

= ^{1 × 2856}/₄₇₆ years

= ²⁸⁵⁶/₄₇₆ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9983 to clear the loan, then find the time period of the loan.

(2) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 4 years.

(4) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.

(5) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 8% simple interest?

(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 4 years.

(7) How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?

(8) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.

(9) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?

(10) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.