Question

A)how much money will you have if you continue this investment for 10 years or 20 yearsB)write an explanation model that represents the amount in the account for any given year

Answer 1

The principal is $5,000.

The growth factor is 1.07.

To create the table, we have to multiply 1.07 by each value in $.

5,000 x 1.07 = 5,350 (1 year).

5,350 x 1.07 = 5,724.50 (2 years).

5,724.50 x 1.07 = 6,125.22 (3 years).

6,125.22 x 1.07 = 6,553.99 (4 years).

6,553.99 x 1.07 = 7,012.77 (5 years).

7,012.77 x 1.07 = 7,503.66 (6 years).

The table would be

Year Money

1 5,350

2 5,724.50

3 6,125.22

4 6,553.99

5 7,012.77

6 7,503.66

Given that this is a geometric sequence, we have

$a_n=a_1\cdot r^{n-1}$

Where the first term is 5,350. Let's find the amount for n = 10.

$a_{10}=5,350\cdot(1.07)^{10-1}=5,350(1.07)^9\approx9,835.76$

After 10 years, we'll get $9,835.76.

Now, for n = 20.

$a_{20}=5,350\cdot(1.07)^{20-1}=5,350(1.07)^{19}\approx19,348.42$

After 20 years, we'll get $19,348.42.

The exponential numbers for any given year would be

$a_n=5,350\cdot(1.07)^{n-1}$