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

Answer:

$ 4075.05

Step-by-step 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 :

$FV = A(\frac{(1+r)^{t}-1}{r}).(1+r)$

$FV = 300(\frac{(1+.055)^{10}-1}{.055}).(1+ .055)$

$FV = 300(\frac{(1.055)^{10}-1}{.055}).(1.055)$

$FV = 300(\frac{1.708144458-1}{.055}).(1.055)$

$FV = 300(\frac{0.708144458}{.055}).(1.055)$

$FV = 300\times 12.875353782\times 1.055$

$FV = 4075.05$

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

Answer 2

.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