Question

A coffee drinker has bought a coffee every morning for $6 per cup for the last several years. She decides to give up coffee and instead save the $6 per day and deposit it at the end of the week ($42 per week) into an account earning 10% compounded weekly (52 weeks per year). If she does this over the next 40 years, how much money will she have accumulated? Show all your work.

please answer will rate

Answer 1

Future value of annuity = P * [(1 + r)ⁿ - 1] / r,

where P = periodic payment. This is $42

r = periodic rate of interest. This is (10%/52). We divide by 52 since we need to convert the annual rate into a weekly rate)

n = number of periods. This is 40 * 52 = 2080 (there are 40 years, or 2080 weeks in the investment period)

Future value of annuity = $42 * [(1 + (10%/52))²⁰⁸⁰ - 1] / (10%/52)

Future value of annuity = $1,166,012.01

She will have accumulated $1,166,012.01 at the end of 40 years