Question

2. Assume someone had $100,000 in their retirement account on 3/3/1/2013. The five year rateof 3.98% means that each year their initial balance will grow by 3.98%. To find out howmuch money they will have in their account five years later we can fill in the following table:Five Year Rate 3.98%DateInitial PrincipalInterestEnding Principal3/31/20133/31/20143/31/20153/31/20163/31/20173/31/2018

Answer 1

Date: 3/31/2013

• Initial principal: ,$100,000

,

• Interest: ,$3,980

,

• Ending principal: ,$103,980

Date: 3/31/2014

• Initial principal: ,$103,980

,

• Interest: ,$4,138.40

,

• Ending principal: ,$108,118.40

Date: 3/31/2015

• Initial principal: ,$108,118.40

,

• Interest: ,$4,303.11

,

• Ending principal: ,$112,421.51

Date: 3/31/2016

• Initial principal: ,$112,421.51

,

• Interest: ,$4,474.38

,

• Ending principal: ,$116,895.89

Date: 3/31/2017

• Initial principal: ,$116,895.89

,

• Interest: ,$4,652.46

,

• Ending principal: ,$121,548.35

Date: 3/31/2018

• Initial principal: ,$121,548.35

Step-by-step explanation

The initial balance is $100,000 and it is said that this balance grows by 3.98% each year. For the first year 3/31/2013 the values are:

• Initial principal: ,$100,000

,

• Interest: here we have to find 3.98% of the initial principal:

`100,000*(3.98)/(100)=100,000*0.0398=3,980`

so the interest is $3,980

• Ending principal: is the initial amount plus the interest of the first year:

`100,000+3,980=103,980`

The ending principal for the first year is $103,980.

Now we have to do the same for the next 4 years. The initial principal will be the ending principal of the previous year. The interest is the 3.98% of the initial principal of the same year and the ending principal is the initial principal plus the interest. So for the second year 3/31/2014:

• Initial principal: ending principal of 2013 = ,$103,980

,

• Interest:

`103,980*(3.98)/(100)\approx4,138.40`

the interest is $4,138.40

• Ending principal:

`103,980+4,138.4=108,118.4`

the ending principal is $108,118.40

Next year, 2015:

• Initial principal: ending principal of 2014 = ,$108,118.40

,

• Interest: 3.98% of initial principal:

`108,118.40\cdot3.98\text{ \%}=4,303.11`

• Ending principal:

`108,118.4+4,303.11=112,421.51`

Year 2016:

• Initial principal: ending principal of 2015 = ,$112,421.51

,

• Interest:

`112,421.51*3.98\text{ \%}=4,474.38`

• Ending principal:

`112,421.51+4,474.38=116,895.89`

Year 2017:

• Initial principal: ending principal of 2016 = ,$116,895.89

,

• Interest:

`116,895.89*3.38\text{ \%}=4,652.46`

• Ending principal:

`116,895.89+4,562.46=121,548.35`

Finally, the initial principal of 2018 is the ending principal of 2017: $121,548.35