Simple Interest
Math MCQs

Question :    Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4700

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

Amount (A) = $7332

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 = $7332 – $4700 = $2632

Thus, Simple Interest = $2632

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 × 2632}/_{4700 × 7}

= ²⁶³²⁰⁰/₃₂₉₀₀

= 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) = $4700

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

Simple Interest = $2632 (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 $4700

= ⁷/₁₀₀ × 4700

= ^{7 × 4700}/₁₀₀

= ³²⁹⁰⁰/₁₀₀ = 329

Thus, simple Interest for 1 year = $329

Now,

∵ If the simple Interest is $329, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₂₉ years

∴ If the simple Interest is $2632, then the time = ¹/₃₂₉ × 2632 years

= ^{1 × 2632}/₃₂₉ years

= ²⁶³²/₃₂₉ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 10% simple interest?

(2) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 7 years.

(3) 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.

(4) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.

(5) 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?

(6) How much loan did Anthony borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7875 to clear it?

(7) In how much time a principal of $3150 will amount to $3276 at a simple interest of 2% per annum?

(8) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.

(9) What amount does David have to pay after 5 years if he takes a loan of $3400 at 4% simple interest?

(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 7 years.