Question

In Year 0, you deposit $5,000 into an account with an interest rate of 6%. Two years later, the interest rate increases to 8%. Five years after that, the interest rate drops to 7%. You plan to withdraw all the money at the end of Year 15. a. At the end of Year 2, how much money is in the account? b. At the end of Year 7, how much money is in the account? c. At the end of Year 15, how much money is in the account? a. At the end of Year 2, how much money is in the account? $ | (Round to the nearest cent - 2 decimal places) b. At the end of Year 7, how much money is in the account? $ (Round to the nearest cent - 2 decimal places) c. At the end of Year 15, how much money is in the account? $ (Round to the nearest cent - 2 decimal places)

Answer 1

Solution a:

Future value after 2 years = $5,000 (1+0.06)^2 = $5,618

Solution b:

Future value after 7 years = $5,618 (1+0.08)^5 = $5,618 * 1.469238 = $8,254.69

Solution c:

Future value after 12 years = $8,254.69 (1+0.07)^8 = $8,254.69 * 1.718186 = $14,183.09

Answer 2

SOLUTION :

a.

Amount deposited at year 0 :

Interest rate for first two years is 6% (0.06 in decimals)

So, Amount at year 2 end :

= 5000 * (1 + 0.06)^2

= 5618 ($) (ANSWER)

b.

Amount in the account at year 2 end = 5618 ($)

Interest rate for next 5 years is 8% (0.08 in decimals)

So, Amount at the end of year 7  :

= 5618 * (1 + 0.08)^5

= 8254.69 ($) (ANSWER)

c.

Amount in the account at year 7 end = 8254.69 ($)

Interest rate for next 8 years (from end of 7 years to end of 15 years) 

is 7% (0.07 in decimals)

So,  Amount at the end of 15 years

= 8254.69 * ( 1 + 0.07)^8

= 14183.09 ($) (ANSWER).