Question

An investment is initially worth $7,000. Write a formula for the value of this investment for each situation described below.

Answer 1

This are simple interest situations.

THe equation for simple interest is:

`V(t)=P(1+Rt)`

Where

t is the time in years

V(t) is the total, the principal amount plus interest

R is the rate of interest

P is the principal value, the amount initially.

in the first case, we have

P = $7000

R = 9% every year

we need to convert it to decimal: 9% / 100 = 0.09

`V(t)=7000(1+0.09t)`

For the second situation:

P = $7000

R = 9% every 7 years

Then, we first convert 9% to decimal: 0.09 and divide it by 7, because we want to express it by t = numer of years.

0.09 / 7 = 9/700

Then equation fo the second case:

`V(t)=7000(1+(9)/(100)t)`

If you The last case:

P = $7000

R = 9% every 1/2 year.

9% to decimal: 0.09 and since this is what the value increases half a year, in a year increases twice, 2 · 0.09 = 0.18

`V(t)=7000(1+0.18t)`