Your wealthy uncle established a $2,200 bank account for you when you were born. For the first 8 years of your life, the interest rate earned on the account was 6%. Since then, rates have been only 4%. Now you are 21 years old and ready to cash in. How much is in your account? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

First of all, you have to calculate the future value of your money with a compound interest rate, but initially you have to calculate the first 8 years with the interest rate of 6% so you have to do the next operation:

Future Value= Present Value *(( 1+ interest rate)^(n))

where n represents the number of years

Future Value= 2.200* (( 1+ 6%)^(8))

Future Value 8 year = $3.506,47

Now that you have that value you need to calculate the money generated in the next 13 years with the same formula but with the new amount of money

Future value 21 year= $3.506,47 *(( 1+4%)^(13))

Future value 21 year= $5.838,52

Finally, you can ask to the bank the $5.838,52 cash

chilljain33 chilljain33 · Answer 2 · 2022-01-19T08:40:36+01:00

The correct statement is that a person will have a compounded annuity of $9347.65 at the end of 21 years on the initial investment of $2200 with interest at 6 percent for the first 8 years and 4 percent for the next 13 years.

The calculation of such compound interest earned will be calculated by addition of two periods of 8 years and 13 years at interest rate of 6 percent and 4 percent respectively.

Compound Annuity

The formula for calculation of compounded annuity is as,

[tex]\rm Compounded\ Annuity= Principal(1+\dfrac{r}{n})^n^t[/tex]

Calculating annuity for both period using the formula,

[tex]\rm Compounded\ Annuity = 2200(1+ 0.06)^8\\\\\rm Compounded\ Annuity =2200 x\ 1.59\\\\\rm Compounded\ Annuity =3507.47[/tex]

Now, for the second period, the annuity for the first period will act as a principal amount. So, the value of annuity will be,

[tex]\rm Compounded\ Annuity = 3507.47(1+0.04)^1^3\\\\\rm Compounded\ Annuity =3507.47 x\ 1.66\\\\\rm Compounded\ Annuity =5840.18[/tex]

Now adding the values of annuities of both the periods, we get the final amount of compounded annuity at the end of 21 years as $9347.65.

Hence, the value of compounded annuity available in the bank account at the end of twenty-one years will be $9347.65 with an initial investment of $2200.

Learn more about compounded annuity here:

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