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

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

Answer 2

$45950.57

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\%=(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.