Question

A graph has years on the x-axis and value of savings on the y-axis. A line with 5.75 percent interest goes through (3, 2,000) and (8, 6,000). A line with no interest goes through (5, 3,000) and (10, 6,000).
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

(a) $6000 this amount is to Arturo’s parents to invest after 10 years. (b) $2083.74 this amount is interest was earned after 10 years. (c) $8346.15 between the amount was earned.

What is interest rate?

An interest rate indicates how expensive borrowing is or how lucrative saving is.

Arturo’s parents deposit $50 each month

Interest rate, r = 5.75%

5.75%/12 = 23/4800 = 0.00479

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

Total Investment = monthly deposits x N

= $50 x 120 = $6000.

$6000 this amount is to Arturo’s parents to invest after 10 years.

FV = Monthly ×$((1+r) ^{120} -1)$/r

FV =  50 ×$\frac{((1+0.00479) ^{120} -1)}{0.00479}$

FV =  $8083.74

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

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

FV = $\frac{((1+0.00479) ^{120} -1)}{0.00479}$

FV = $\frac{((1+0.00479) ^{240} -1)}{0.00479}$

FV=  $22429.89

Interest Earned in 20 years = $22429.89—$12000 = $10429.89.

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

As a result, a) $6000 b) $2083.74 c) $8346.15 is an accurate answer.

Learn more about on interest rate, here:

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