Question

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

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

b. What will the value be after 10 years?

Answer 1

a)

`A\:=\:P\left(1\:+\:(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.

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\:+\:(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\:+\:(r)/(n)\right)^(nt)`

substituting the values

`A\:=\:4200\left(1\:+\:(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.