Simple Interest
Math MCQs

Question :    Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5500

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

Amount (A) = $7810

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 = $7810 – $5500 = $2310

Thus, Simple Interest = $2310

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 × 2310}/_{5500 × 7}

= ²³¹⁰⁰⁰/₃₈₅₀₀

= 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) = $5500

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

Simple Interest = $2310 (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 $5500

= ⁷/₁₀₀ × 5500

= ^{7 × 5500}/₁₀₀

= ³⁸⁵⁰⁰/₁₀₀ = 385

Thus, simple Interest for 1 year = $385

Now,

∵ If the simple Interest is $385, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₈₅ years

∴ If the simple Interest is $2310, then the time = ¹/₃₈₅ × 2310 years

= ^{1 × 2310}/₃₈₅ years

= ²³¹⁰/₃₈₅ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 4 years.

(2) If Paul paid $5640 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(3) How much loan did Karen borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6545 to clear it?

(4) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 2% simple interest?

(5) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 8 years.

(6) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.

(7) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 5% simple interest?

(8) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 4 years.

(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 7 years.

(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 7 years.