# Math Help - Annuities/Compound Interest 10 questions

1. ## Annuities/Compound Interest 10 questions

Can anyone help me out w/these?

1. A 1 year $100,000 T-bill sells at a discount rate of 3.25%. What simple annual interest rate does it pay. (Round to the nearest 100th of a percent.) a. 3.36% b. 3.14% c. 3.25% d. None of these 2. If$10,000 is deposited in a money market account when interest is compounded every month at an annual rate of 5%, the total amount accumulated at the end of 5 years will be: (Round to the nearest cent.)

a. $12,762.82 b.$10,210.08

c. $12,833.59 d. None of these 3.. If you invest$5,000 at 4% compounded semiannually, how long will it take for your investment to grow to $8,000? (Round to the nearest year.) a. 10 years b. 24 years c. 6 years d. None of these 4.. How much would you have to invest when you are 20 years old at 6% compounded monthly to end up with a million dollars by age 50? (Round up to the nearest thousand.) a.$862,000

b. $167,000 c.$175,000

d. None of these

5. If you deposit $4,000 in a money market account when interest is compounded quarterly, what annual rate of interest would be required to end up with$8,000 in 5 years? (Round to the nearest 10th of a percent.)

a. 13.9%

b. 14.1%

c. 14.7%

d. None of these

6. How much should we deposit now into an account earning 6% interest per year, compounded monthly so that starting one month from now the bank will send us monthly payments of $200 for 5 years? At the end of the five years, the account balance should be depleted to zero. (Round to the nearest cent.) a.$11,280.00

b. $10,396.84 c.$10,345.11

d. None of these

7. How much should be deposited now in an account earning 4.2% interest per year, compounded quarterly so that starting 3 months from now the bank will send us quarterly payments of $150 for 10 years? At the end of that time we would like to have$2,000 left in the account. (Round to the nearest cent.)

a. $6,246.96 b.$6,195.73

c. $4,878.76 d. None of these 8.. A newspaper carries advertisements for CD rates / terms for four local banks. Which would be the best deal? a. Scrooge Investments -- 4.00% compounded daily b. Cloverdale Bank & Trust -- 4.10% compounded quarterly c. Omega Savings & Loan -- 4.00% compounded quarterly d. Worker’s Credit Union -- 4.10% compounded annually 9. Midwest Bank & Trust advertises a CD that pays 4.9% APY compounded monthly. What is the effective interest rate? (Round to the nearest 10th of a percent.) a. 4.8% b. 4.9% c. 5.0% d. None of these 10. What would it cost to buy a U.S. Treasury bill that pays$10,000 after 6 months where the simple annual interest rate is 3.75%? (Round to the nearest cent.)

a. $9,625.45 b.$9,812.50

c. $9,815.95 d. None of these 2. Let's try these one at a time.. 1. A 1 year$100,000 T-bill sells at a discount rate of 3.25%. What simple annual interest rate does it pay. (Round to the nearest 100th of a percent.)

a. 3.36%

b. 3.14%

c. 3.25%

d. None of these
The amount of the the T-bill is irrelevant. I assume the discount rate is simple as well.

$1 - d = \frac{1}{i+1}$
$1 + i = \frac{1}{1-d}$
$i = \frac{d}{1-d} = \frac{.0325}{1-.0325} = .0336$

3. Originally Posted by colby2152
Let's try these one at a time..

The amount of the the T-bill is irrelevant. I assume the discount rate is simple as well.

$1 - d = \frac{1}{i+1}$
$1 + i = \frac{1}{1-d}$
$i = \frac{d}{1-d} = \frac{.0325}{1-.0325} = .0336$

0.0336 is 3.36%

RonL

4. 2. If $10,000 is deposited in a money market account when interest is compounded every month at an annual rate of 5%, the total amount accumulated at the end of 5 years will be: (Round to the nearest cent.) a.$12,762.82

b. $10,210.08 c.$12,833.59

d. None of these

$1 + I = (1 + \frac{i}{m})^{mt}$

Therefore, the accumulation is:

$A = 10,000(1 + \frac{.05}{12})^{12*5} = 12,833.59$

5. Originally Posted by JP101
3.. If you invest $5,000 at 4% compounded semiannually, how long will it take for your investment to grow to$8,000? (Round to the nearest year.)

a. 10 years

b. 24 years

c. 6 years

d. None of these
Similar to the last problem, but we are solving for time. Also note that this is 4% semiannual interest rate. No where in the problem do you see the word annual.

$8,000 = 5,000(1.04)^{t/2}$
$ln(1.6) = \frac{tln(1.04)}{2}$
$.47 = .0196t$
$t = 23.97$ years