Suppose Hali, an 18-year-old decides to invest $2000 per year for ten years into an account that averages an annual return of 12%. After the tenth year she then lets the money stay in the account, but makes no further payments to the account, until she is 70 (retirement age). Ten years before retirement this investor will move the money to a more secure investment that has an average annual return of 6%. How much money will she have in the account to use in her retirement years? How much total money did she invest?
Answers
Answer:
She will have $73,154 approximately in her account to use in her retirement years.
The total money she invested is $26,212 approximately.
Step-by-step explanation:
Here I will explain how I got this.
Explanation: -
She invested $2000 per year for 10 years at the annual return rate of 12%. For the interest amount after 10 years, we will use below formula: -
P x 〖(1+ R/N)〗^nt
P = Principle amount = $2000
R = Interest rate in decimal = 0.12
N = Number of times interest rate is compounded per year = 1
NT = Time = 10 years
P x 〖(1+ R/N)〗^nt = 2000 x〖(1+ 0.12/1)〗^10 = $6,212 approximately
The total amount she will have in her account after 10 years = Principle Amount + Compound Interest = 2000 x 10 years + 6212 = $26,212
After 10 years, she will have $26,212 approximately.
She will invest $6,212 as per the advice of the investor at the annual return rate of 6%. For the compound amount after 10 years, we will use below formula: -
P x 〖(1+ R/N)〗^nt
P = Principle amount = $26,212
R = Interest rate in decimal = 0.06
N = Number of times interest rate is compounded per year = 1
NT = Time = 10 years
P x 〖(1+ R/N)〗^nt = 26,212 x〖(1+ 0.06/1)〗^10 = $46,942 approximately
The total amount she will have in her account at retirement age = Principle Amount + Compound Interest = 26,212 + 46,942 = $73,154
She invested $73,154 approximately.
Total money she invested = $26,212 approximately