Question

Question 8 0/1 pts Suppose that each week, you deposit $65 in a bank account whose annual rate is 1.5% with weekly compounding. How much interest will you earn after 10 years? Round your answer to the nearest dollar. Answered 2311.0000 ect Answer 2661.0 margin of error+-50.0

How did they get the answer of 2661? (in order of steps please!)

Answer 1

Total interest earned = Accumulated amount - Pricipal amount

First we calculate accumulated amount (A)

A = P [ (1+r/n)^n*t - 1 / (r/n) ]

Where P = amount invested = 65

r = rate per year = 0.015

n = number of periods(weeks) per years = 52

t = time in year.

A = 65 [ (1 + 0.015/52)^52*10 - 1 / (0.015 / 52) ]

= 65 [ (1.000288762)⁵²⁰ - 1 / (0.015 / 12) ]

= 65 [ 0.161809 / (0.015 / 12) ]

= 36460.99

$\approx$ 36461

Principal amount = Weekly payment * number of weeks in years * number of years

= 65 * 52 * 10

= 33800

Interest amount = 36461 - 33800

= 2661

Interest earned = 2661.0