Question

please show your work and solve for 16-18

Problems with a little twist (i-6% unless otherwise stated) 16. If $10000 is deposited today with annual interest rate of 6% and each month is desired to withdraw from this account $100, how many times this monthly withdrawals can be done before the money runs out? 17. If we deposit $100 a month for the next 5 years into an account and at the end of 5 years the account has accumulated $10,000 what is the interest rate earned on this account? 18. If we deposit $100 a month into an account which earns 6% interest annually, for 5 consecutive years, how much money exists in this account after ten years? 19. If $100 is deposited into an account from years 1-5, then from years 6-10 nothing is deposited. From years 11-15 again $100 is deposited into that account. How much money is accumulated after the end of 20th year? i 6%. 20. If you borrow $10,000 today. Then pay $5000 at the end of 5 years and you decide to

Answer 1

16.

We have, Deposit = $10000 , Annual interest rate = 6% and Monthly withdraw = $100 . we can calculate how many times this monthly withdrawals can be done before the money runs out, by using the following formula:

solving for N, we get N=11.33 . since N is number of years withdrawals can done, so in terms of months it would be 136 months.Therefore, 136 months/times this monthly withdrawals can be done before the money runs out.

17.

The interest rate earned on this account can be calculated by using this formula:

15 (5)12 -1

Solving for r, we get r = 20%. which means, if we deposit $100 a month for next 5 years into an account and at the end of 5 years we get $10,000, the interest rate earned on this account would be 20%.

18.

For calculating the interest rate ,we can use the following formula:

for 5 years P_N is $7000. and now we can use the compound interest formula to calculate, amount exists in this account after 10 years. The amount exists in this account after 10 years is $9367.