Simple Interest
Math MCQs

Question :    Jessica took a loan of $5500 at the rate of 6% 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  7

Solution & Explanation

Solution

Given,

Principal (P) = $5500

Rate of Simple Interest (R) = 6% 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 × 6}

= ²³¹⁰⁰⁰/₃₃₀₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = 6% 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 = 6% of Principal

= 6% of $5500

= ⁶/₁₀₀ × 5500

= ^{6 × 5500}/₁₀₀

= ³³⁰⁰⁰/₁₀₀ = 330

Thus, simple Interest for 1 year = $330

Now,

∵ If the simple Interest is $330, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₃₀ years

∴ If the simple Interest is $2310, then the time = ¹/₃₃₀ × 2310 years

= ^{1 × 2310}/₃₃₀ years

= ²³¹⁰/₃₃₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.

(2) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?

(3) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 6% simple interest?

(4) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 8% simple interest.

(5) How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?

(6) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 7% simple interest?

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

(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 4 years.

(9) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 3% simple interest?

(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 8 years.