Question

A high interest savings account pays 5.5% interest compounded annually. If $300 is deposited initially and again at the first of each year, which summation represents the money in the account 10 years after the initial deposit

Answer 1

.The amount of $300 is deposited in the account for 10 years from the date of initial deposit.

The Interest rate in the account is 5.5%

Total summation of money in the account after 10 years is given by the following equation = 300 * ((1.055)^10 - 1 ) / 0.055 * ( 1 + 0.055 )

= 300 * (.0.708144)/0.055 * 1.055

= 4075.05

Total money in account after 10 years is $ 4075.05

The Summation sign that can be used to express the equation is

∑3000*(1.055 )^x , where x assumes values from 1 to 10

Answer 2

$ 4075.05

Explanation:

Given :

R = Interest rate = 5.5%

T = Duration of Payment = 10 years

FV = Future Value

A = Amount

The amount of deposited in the account for 10 years from the date of initial deposit is $300

We are given that the Interest rate in the account is 5.5%

So by formula :

`FV = A(((1+r)^(t)-1)/(r)).(1+r)`

`FV = 300(((1+.055)^(10)-1)/(.055)).(1+ .055)`

`FV = 300(((1.055)^(10)-1)/(.055)).(1.055)`

`FV = 300((1.708144458-1)/(.055)).(1.055)`

`FV = 300((0.708144458)/(.055)).(1.055)`

`FV = 300* 12.875353782* 1.055`

`FV = 4075.05`

Thus , Total summation of money in the account after 10 years is given by the following equation =$ 4075.05

Total money in account after 10 years is $ 4075.05