Question

Arturo's parents deposit $50 each month into a college savings account with a 5.75% interest rate, compounded monthly. About how much money did Arturo's parents invest after 10 years? About how much interest was earned after 10 years? Between 10 years and 20 years, how much more interest would you expect the account to earn?

Answer 1

Answer:

$6,000

$2,000

More than $2,000

Step-by-step explanation:

Answer 2

Answer:

a) $6000

b) $2083.74

c) $8346.15

Step-by-step explanation:

Monthly Deposits, Pmt = $50

Interest rate, r = 5.75%/12 = 23/4800 = 0.00479

In 10 years, tenure, N = 10 x 12 = 120 months.

Total Investment = $50 x 120 = $6000.

$FV = \frac{Pmt*[(1+r)^N -1]}{r}\\\\FV = \frac{50*[(1+0.00479)^{120} -1]}{0.00479}\\\\FV = \ 8,083.74$

Interest Earned in 10 years = $8083.74 - $6000 = $2083.74

If they continue to invest for 20 years, tenure = 12 x 20 = 240 months.

$FV = \frac{Pmt*[(1+r)^N -1]}{r}\\\\FV = \frac{50*[(1+0.00479)^{240} -1]}{0.00479}\\\\FV = \ 22,429.89$

Interest Earned in 20 years = $22429.89 - $12000 = $10429.89

Interest Earned between 10 years and 20 years = $10429.89 - $2083.74 = $8346.15