Question

You would like to save annually for buying a car 6 years from today. Suppose the first deposit is made today and the last deposit will be made 5 years from now. Assume the car will cost you $30,000 and your deposits earn you interest at 6% p.a, compounded annually.

(a) What is your annual deposit amount?

(b) Instead of making annual deposits, you would like to make your deposit monthly and the bank is happy to pay your interest on a monthly basis. What is the APR that would make the bank indifferent to these two way of paying interest?

(c) Assuming you make the deposit of $300 at the end of each month and the first deposit will be made one month from today, use the answer to part (b) calculate how much your deposits would accumulate to 6 years later.

(d) Assume 6 years later, the car price has gone up to $35,000. You decide to use the accumulated deposit as the down payment and take up a 2-year car loan. What would your monthly payment be if the interest rate is 7.5% and compounded monthly?

Answer #1

a] | Annual deposit = 30000*(0.06)/((1.06)*(1.06^6-1) = |
$
4,057.43 |

b] | 6% should be the effective interest rate | |

So, 0.06 = (1+r)^12-1, where t = APR/12 | ||

r = (0.06+1)^(1/12)-1 = | 0.486755% | |

APR = r*12 = | 5.84% | |

c] | FV = 300*((1+0.0584/12)^72-1)/(0.0584/12) = |
$
25,793.59 |

d] | Loan amount = 35000-25793.59 = | $ 9,206.41 |

Monthly payment = 9206.41*(0.0584/12)*(1+0.0584/12)^24/((1+0.0584/12)^24-1) = |
$
407.37 |

You would like to have $73,000 in 14 years. To accumulate this
amount, you plan to deposit an equal sum in the bank each year that
will earn 9 percent interest compounded annually. Your first
payment will be made at the end of the year.
a. How much must you deposit annually to accumulate this
amount?
b. If you decide to make a large lump-sum deposit today
instead of the annual deposits, how large should the lump-sum
deposit be? ...

1. You would like to have $50,000 in 15 years. To accumulate
this amount you plan to deposit each year an equal sum in the bank,
which will earn 7% interest annually. Your first payment will be
made at the end of the year. o How much must you deposit annually
to accumulate this amount? o If you decide to make a large lump-sum
deposit today instead of the annual deposits, how large should this
lump-sum deposit be? o At...

You would like to have $41,000 in 15 years. To accumulate this
amount, you plan to deposit each year an equal sum in the bank,
which will earn 7 percent interest compounded annually. Your first
payment will be made at the end of the year.
At the end of 4 years you will receive $9,000 and deposit this
in the bank toward your goal of $41,000 at the end of 15 years. In
addition to this deposit, how much must...

Q1) Suppose you invest $66,624 today in an account that earns
13.00% interest annually. How much money will be in your account 11
years from today?
Q2) What is the value today, of single payment of $51,252 made
13 years from today, if the value is discounted at a rate of
04.00%?
Q3) How many years would it take an investment of $333 to grow
to $10,789 at an annual rate of return of 11.00%?
Q4) How much money would...

A. Suppose you invest $83736 today in an account that earns 13%
interest annually. How much money will be in your account 7 years
from today?
B. What is the value today of single payment of $36665, 18 years
from today if the value is discounted at a rate of 19%?
C. How many years would it take an investment of $172 to grow to
$18096 at an annual rate of return of 15%?
D. How much money would you...

Assume that you would like to make 6 yearly deposits for your
kid’s college tuition fee starting today. The initial deposit for
today is $10000 dollars and each year the amount increases by
$1000. The interest rate is assumed to be 8% per year.
a) Draw the cash flow diagram (CFD).
b) Assuming that your kind needs the tuition money as a
lump-sum amount, 10 years from now.
Find the total amount of money that will be accumulated in the...

What is the present value of $10,000 to be received 10
years from today, assuming a 6 percent annual interest (discount)
rate?
2. If you
deposit $3,000 in a bank account that pays 4 percent annual
interest, what would your account balance equal after 9
years?
3. To
settle a wrongful death case, a judge ordered the maker of a
defective product to pay the spouse of the deceased person $100,000
today, $150,000 four years from today, and $250,000 eight...

(Nonannual compounding using a calculator) Jesse Pinkman is
thinking about trading cars. He estimates he will still have to
borrow $30,000 to pay for his new car. How large will Jesse's
monthly car loan payment be if he can get a 7-year (84 equal
monthly payments) car loan from the university's credit union at
an APR of 7.1 percent compounded monthly?
Jesse's monthly car loan payment will be $ (Round to the
nearest cent.)
(Compound annuity) You plan on...

Six years from today you need $10,000. You plan to deposit
$1,400 annually, with the first payment to be made a year from
today, in an account that pays a 9% effective annual rate. Your
last deposit, which will occur at the end of Year 6, will be for
less than $1,400 if less is needed to reach $10,000. How large will
your last payment be? Do not round intermediate calculations. Round
your answer to the nearest cent.
$ =

Six years from today you need $10,000. You plan to deposit
$1,400 annually, with the first payment to be made a year from
today, in an account that pays a 10% effective annual rate. Your
last deposit, which will occur at the end of Year 6, will be for
less than $1,400 if less is needed to reach $10,000. How large will
your last payment be? Do not round intermediate calculations. Round
your answer to the nearest cent.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 38 seconds ago

asked 40 seconds ago

asked 2 minutes ago

asked 3 minutes ago

asked 6 minutes ago

asked 8 minutes ago

asked 9 minutes ago

asked 11 minutes ago

asked 14 minutes ago

asked 18 minutes ago

asked 18 minutes ago

asked 19 minutes ago