Question

If the Laffite family deposits $8500 in a savings account at 6.75% interest, compounded continuously, how much will be in the account after 25 years?

Answer 1

Answer:

$45950.57

Step-by-step explanation:

We have been given that the Laffite family deposits $8500 in a savings account at 6.75% interest, compounded continuously.

To find the amount in the account after 25 years we will use continuous compounded interest formula.

$A=P*e^{rt}$,where,

A = Final amount after t years,

P = Principal amount,

e = Mathematical constant,

r = Interest rate in decimal form,

t = Time.

Let us convert our given rate in decimal form.

$6.75\%=\frac{6.75}{100}=0.0675$

Upon substituting our given values in above formula we will get,

$A=\ 8500*e^{0.0675*25}$  

$A=\ 8500*e^{1.6875}$  

$A=\ 8500*5.405948925141167$

$A=\ 45950.5658636999195\approx\ 45950.57$  

Therefore, there will be $45950.57 in the account after 25 years.

Answer 2

With compounded continuously the formula is
A=pe^rt
A future value?
P present value 8500
R interest rate 0.0675
T time 25 years
E constant

A=8,500×e^(0.0675×25)
A=45,950.57