Question

What lump sum deposited today at 8 ?% compounded quarterly for 15 years will yield the same final amount as deposits of ?$6000 at the end of each? 6-month period for 15 years at 8 ?% compounded? semiannually?

The value of the lump sum is?

Answer #1

$
1,02,562.17 |

Working:

a. | Calculate future value of 6-month deposits | |||||||||||

Future Value | = | 6-month deposits x future Value of 6-month deposits for 15 years | ||||||||||

= | $ 6,000.00 | x | 56.08494 | |||||||||

= | $ 3,36,509.63 | |||||||||||

Working: | ||||||||||||

Future Value of 6-month deposits for 15 years | = | (((1+i)^n)-1)/i | Where, | |||||||||

= | (((1+0.04)^30)-1)/0.04 | i | 4% | |||||||||

= | 56.08494 | n | 30 | |||||||||

b. | Present Value of amount to be deposited | |||||||||||

Present Value | = | F*(1+i)^-n | Where, | |||||||||

= | 336509.63*(1+0.02)^-60 | i | 8%/4 | = | 0.02 | |||||||

= | $ 1,02,562.17 | n | 15*4 | = | 60 | |||||||

F | = | $ 3,36,509.63 | ||||||||||

What lump sum deposited today at 8% compounded quarterly for 5
years will yield the same final amount as deposits of $3000 at the
end of each 6-month period for 5 years at 4% compounded
semiannually?

What lump sum deposited today at 12% compounded quarterly for 5
years will yield the same final amount as deposits of $5000 at the
end of each 6-month period for 5 years at 8% compounded
semiannually?

What lump sum deposited today at 12% compounded quarterly for
10 years will yield the same final amount as deposits of $4000 at
the end of each 6-month period for 10 years at 10% compounded
semiannually?

What lump sum of money must be deposited into a bank account at
the present time so that $600 per month can be withdrawn for six
years, with the first withdrawal scheduled for seven years from
today? The interest rate is 1/2% per month. (Hint: Monthly
withdrawals begin at the end of the month 84.)

1. For the next 6 years, you pan to make equal quarterly
deposits of $600.00 into an account paying 8% compounded quarterly.
How much will be the total you have at the end of the time?
2. How much money will you have to deposit now if you wish to
have $5,000 at the end of 8 years. Interest is to be at the rate of
6% compounded semiannually?
3. In the California “Million Dollar Lottery” a winner is paid...

Time Value of Money
What is the present value of a $2,000 lump sum to be paid in
six years if interest rate is
5%?
Suppose you deposit $1,000 today in an account that pays 8%
APR. How many yearswill it take the account
balance to grow to $3,000 if interest is compounded quarterly?

Find the least amount that could be deposited in a bank account
today at 10% compounded semiannually to allow $1875 withdrawals at
the end of each 6 months for 12 years. Round to the nearest
cent
A 26,426.14
B 25,872.45
C 49,127.55
D 25,291.07

A sum of $25,000 is deposited into a savings account, which pays
8% interest
compounded semiannually. Equal annual withdrawals are to be made
from the account,
beginning 1 year from now and continuing forever. The maximum
amount that can be
withdrawn at the end of each year is approximately equal to
____________.
A) $2,250
B) $2,000
C) $2,300
D) $2,040

SINGLE LUMP-SUM Below are four independent scenarios relating to
the investment of a single lump-sum amount. Calculate the future
value of each, using the algebraic formula illustrated in the
textbook. Then, verify your answer by reference to the “future
value of $1” table. If you have a “business” calculator,
additionally verify your calculations using the future value
functions included with your calculator.
a) An investment of $2,000 for 6 years and then also for 8
years, at a 6% annual...

$300 is deposited in an account which earns 4% compounded
quarterly for 6.75 years.
(a) State the value of the account at the end of the 6.75
years.
$
(b) State the total amount of interest earned on the account during
the 6.75 years.
$

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