Simple Interest
MCQs Math

Question:     Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution And Explanation

Solution

Given,

Principal (P) = $5300

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $8480

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 = $8480 – $5300 = $3180

Thus, Simple Interest = $3180

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 × 3180}/_{5300 × 6}

= ³¹⁸⁰⁰⁰/₃₁₈₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = $5300

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $3180 (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 $5300

= ⁶/₁₀₀ × 5300

= ^{6 × 5300}/₁₀₀

= ³¹⁸⁰⁰/₁₀₀ = 318

Thus, simple Interest for 1 year = $318

Now,

∵ If the simple Interest is $318, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₁₈ years

∴ If the simple Interest is $3180, then the time = ¹/₃₁₈ × 3180 years

= ^{1 × 3180}/₃₁₈ years

= ³¹⁸⁰/₃₁₈ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 9% simple interest?

(2) How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?

(3) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 9% simple interest?

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

(5) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 3 years.

(6) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.

(7) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 2% simple interest?

(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 8 years.

(9) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.

(10) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12800 to clear the loan, then find the time period of the loan.