Simple Interest
Math MCQs

Question :    In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?

Correct Answer  2

Solution & Explanation

Solution

Given,

Principal (P) = $3050

Rate of Simple Interest (R) = 5% per annum

Amount (A) = $3355

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 = $3355 – $3050 = $305

Thus, Simple Interest = $305

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 × 305}/_{3050 × 5}

= ³⁰⁵⁰⁰/₁₅₂₅₀

= 2 years (using formula)

Thus, Time (T) = 2 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) = $3050

Rate of Simple Interest (R) = 5% per annum

Simple Interest = $305 (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 = 5% of Principal

= 5% of $3050

= ⁵/₁₀₀ × 3050

= ^{5 × 3050}/₁₀₀

= ¹⁵²⁵⁰/₁₀₀ = 152.5

Thus, simple Interest for 1 year = $152.5

Now,

∵ If the simple Interest is $152.5, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/_152.5 years

∴ If the simple Interest is $305, then the time = ¹/_152.5 × 305 years

= ^{1 × 305}/_152.5 years

= ³⁰⁵/_152.5 = 2 years

Thus, time (T) = 2 years Answer

Similar Questions

(1) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.

(2) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 7% simple interest?

(3) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?

(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.

(5) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9360 to clear it?

(6) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 5% simple interest?

(8) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.

(9) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 7 years.

(10) What amount will be due after 2 years if David borrowed a sum of $3200 at a 8% simple interest?