Question

The principal amount, $4200, earns 3.6% interest compounded monthly.

Answer 1

Answer:

a)

$A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}$

b)

The total amount accrued, principal plus interest,  from compound interest on an original principal of  $ 4,200.00 at a rate of 3.6% per year  compounded 12 times per year  over 10 years is $5667.28.

Step-by-step explanation:

a. Write the function that represents the value of the account at any time, t.

The function that represents the value of the account at any time, t

$A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}$

where

P represents the principal amount

r represents Annual Rate

n represents the number of compounding periods per unit t, at the end of each period

t represents the time Involve

b) What will the value be after 10 years?

Given

The principal amount  P = $4200

Annual Rate r = 3.6% = 3.6/100 = 0.036

Compounded monthly = n = 12

Time Period = t

To Determine:

The total amount A = ?

Using the formula

$A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}$

substituting the values

$A\:=\:4200\left(1\:+\:\frac{0.003}{12}\right)^{\left(12\right)\left(10\right)}$

$\:A\:=\:4200\left(1.0025\right)^{120}$

$A=5667.28$ $

Therefore, the total amount accrued, principal plus interest,  from compound interest on an original principal of  $ 4,200.00 at a rate of 3.6% per year  compounded 12 times per year  over 10 years is $5667.28.