105k views
2 votes
$1,200 are deposited into an account with

a 6.75% interest rate, compounded
quarterly.
Find the accumulated amount after
20 years.
Hint: A = P(1+r/k)^kt

User Ciaranc
by
9.0k points

2 Answers

7 votes

Answer: 4577.06

Work Shown:

A = P(1+r/k)^(kt)

A = 1200(1+0.0675/4)^(4*20)

A = 4577.06277131092

A = 4577.06

User Jonathon Hibbard
by
8.1k points
1 vote

Answer:

Accumulated amount =$4577.062771

Explanation:

Given:

  • Principal(p) = $1,200
  • Interest rate(r) = 6.75% per year = 0.0675
  • Number of years (t) = 20 years
  • Number of compounding periods per year (k) = 4

Formula:

The formula for compound interest is:


\sf A = P\left(1 + (r)/(k)\right)^(kt)

where:

  • A is the accumulated amount
  • P is the principal
  • r is the interest rate
  • k is the number of compounding periods per year
  • t is the number of years

Solution:

Substitute the given values, we get:


\sf A = 1,200\left(1 + (0.0675)/(4)\right)^(4* 20)

Evaluating the expression in the calculator, we get:


\sf A = 1,200\left(1 + 0.016875\right)^(80)


\sf A = 1,200\left(1.016875\right)^(80)


\sf \sf A = 1,200*3.814218976


\sf A = 4577.062771

Therefore, the accumulated amount after 20 years is $4577.062771.

User Adam Calvet Bohl
by
8.6k points