Simple Interest
Math MCQs

Question :    Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8364 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5100

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $8364

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 = $8364 – $5100 = $3264

Thus, Simple Interest = $3264

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 × 3264}/_{5100 × 8}

= ³²⁶⁴⁰⁰/₄₀₈₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $5100

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $3264 (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 = 8% of Principal

= 8% of $5100

= ⁸/₁₀₀ × 5100

= ^{8 × 5100}/₁₀₀

= ⁴⁰⁸⁰⁰/₁₀₀ = 408

Thus, simple Interest for 1 year = $408

Now,

∵ If the simple Interest is $408, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₀₈ years

∴ If the simple Interest is $3264, then the time = ¹/₄₀₈ × 3264 years

= ^{1 × 3264}/₄₀₈ years

= ³²⁶⁴/₄₀₈ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.

(2) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8507 to clear the loan, then find the time period of the loan.

(3) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 4% simple interest?

(4) If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(5) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 4 years.

(6) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6888 to clear the loan, then find the time period of the loan.

(7) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.

(8) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 7% simple interest?

(9) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 9% simple interest.

(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 8 years.