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I NEED HELP QUICKLY PLEASE PLEASE PLEASE

John wants to have $2 000 in 3 years. The current rate of return for a high interest savings
account is 2.8%, compounded annually. The money, P dollars, that John must invest now is given by the formula P initial investment = 2 000 (1.028) -3, where the exponent of the power is the time, in years.

a. How much must John invest now to have $2 000 in 3 years?


b. Assuming the interest rate remains consistent, how much money will John have in 5 years
if he doesn’t touch the investment after the initial 3 years? Hint: The original formula will
have to change.

Respuesta :

a. you plug in to a calculator, which will give 1840.986 so you need to round up to 1840.99. if you truncate it to .98 then he won't reach 2000 in 3 years

b. for this one if you look at the equation given to find the principle it is principle = result (1+rate) ^ -time

if you re arrange this you get result=principle (1+rate)^time
so result = 1840.99(1.028)^5
= 2113.57

Answer:

The compound interest formula is :

[tex]A=p(1+\frac{r}{n})^{nt}[/tex]

Now, we have to find p.

A = 2000

r = 2.8% or 0.028

n = 1

t = 3

Putting the values in formula we get;

[tex]2000=p(1+\frac{0.028}{1})^{3}[/tex]

=> [tex]2000=p(1.028)^{3}[/tex]

=> [tex]2000=p(1.08637)[/tex]

=> [tex]2000/1.08637=p[/tex]

So, p = $1840.99 rounded to $1841.

Part A: John should invest $1841 now to have $2000 in 3 years.

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Part B:

Now p = 1841

r = 0.028

n = 1

t = 5

[tex]A=1841(1+\frac{0.028}{1})^{5}[/tex]

=> [tex]A=1841(1.028)^{5}[/tex]

=> [tex]A=1841(1.1480)[/tex]

A = $2113.46

Hence, John will have $2113.46 in 5 years.

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