Question

In: Finance

Quarterly deposits are made into a fund at the beginning of each quarter starting today for...

Quarterly deposits are made into a fund at the beginning of each quarter starting today for 5 years. The first 8 deposits are $1000 each and deposits increase by 1% per quarter thereafter. If the fund earns 8% effective annually, find the accumulated value at the end of 5 years.

Please explain which equations you used and do not use excel.

Solutions

Expert Solution

Quartertly deposits for 2 years = $1,000

Growth rate of Quarterly deposits after 2 years = 1%

Effective Interest rate = 8%

where r is the nominal quarterly rate

m is the number of compounding periods

i is the effective interest rate

r = 0.07771/4 = 0.01943 or 1.943%

The equation to find out future value of deposits is given below

Where F is the future value

P is the deposit

r is the quarterly interest rate

m is the total number of compounding periods (Quarters)

Number of quarters in first two years = 2*4 = 8

Value of deposits for the first two years =

Value of deposits for the first two years = $8565.70

The equation for the future value of a growing annuity is given below

where g is the growth rate

Number of quarters after two years = 3*4 = 12

growth rate = 1% = 0.01

Future Value after two years is equal to:

Future Value after two years = $14,097.37

Total Value after 5 years = $8,565.70 + $14,097.37 = $22,663.07

jeff jeffy answered 1 year ago

Next > < Previous

Related Solutions

Bob deposits $1,500 at the beginning of each quarter for sixteen years in a fund earning...

Bob deposits $1,500 at the beginning of each quarter for sixteen years in a fund earning a nominal rate of interest of 6% convertible monthly. The interest from this fund is paid out monthly and can only be reinvested at an effective annual rate of 5.2%. Find Bob’s yield rate for the twenty-year period.

what quarterly deposits at the end of each quarter should be made into a savings account paying the nominal interest of

1. what quarterly deposits at the end of each quarter should be made into a savings account paying the nominal interest of 4% compounded quarterly to accumulate $10,000 at the end of 10 years?2. Faith buys a used car by paying a $500 down payment plus $180 a month for 3 years. what was the price of the car if the interest rate on the loan is the nominal interest rate of 9% compounded monthly?

If you make 20 quarterly deposits of $1,000 beginning today and are earning 6% APR (compounded...

If you make 20 quarterly deposits of $1,000 beginning today and are earning 6% APR (compounded monthly), how much will the account be worth 20 quarters from today?

Claude made annual deposits of $5900 at the beginning of every one-year period into a fund...

Claude made annual deposits of $5900 at the beginning of every one-year period into a fund earning 3.1% compounded annually for eight years. No further deposits were made.(a) How much will be in the account seventeen years after the first deposit? (b) How much in total was deposited? (c) How much interest will have been earned? a) The balance in the account seventeen years after the first deposit will be $____. (Round the final answer to the nearest cent as...

Starting today, a series of annual deposits is made into an account offering 8 percent compounded annually.

Starting today, a series of annual deposits is made into an account offering 8 percent compounded annually. The first deposit is $2,000. The second deposit is 2 percent smaller than the first, that is, $2,000 (0.98)^1. The third deposit is 2 percent smaller than the second, that is, $2,000 (0.98)^2. This pattern of declining deposits, with each deposit being 2 percent smaller than the previous one, continues until the last deposit is made at the end of year 40, that...

Milo deposits $500 at the beginning of each year for 2 years into a fund that...

Milo deposits $500 at the beginning of each year for 2 years into a fund that earns 8% annual effective. Half of the interest is reinvested at 10% annual effective and the remaining half is reinvested in Milo’s pocket (at 0%). Calculate the accumulated value in all three accounts in 10 years. No excel solution please

Emily deposits $150 at the beginning of each quarter into an account earning 6.7% for 25...

Emily deposits $150 at the beginning of each quarter into an account earning 6.7% for 25 years. How much money will she have at the end of those 25 years?

Deposits of $425 are made quarterly in an investment. The first deposit is made on February...

Deposits of $425 are made quarterly in an investment. The first deposit is made on February 15, 2014 and the last deposit is made on August 15, 2024. Find the nominal rate converted quarterly that is earned if the account balance just after the last deposit on August 15, 2024 is $28966.54.

Nataya makes monthly deposits into Fund A at the beginning of each month for 25 years....

Nataya makes monthly deposits into Fund A at the beginning of each month for 25 years. Her first deposit is $40, and each subsequent deposit increases by $10. Aarif contributes $250,000 once, today, into Fund B. The nominal rate that both of these funds earn is 6% per year. However, Fund A compounds interest monthly and Fund B compounds interest quarterly. What is the difference in the balance between these two funds at the end of 25 years?

Bob deposits $11000 at the beginning of each year for six years in a fund earning...

Bob deposits $11000 at the beginning of each year for six years in a fund earning an effective annual rate of 6.7%. The interest from this fund can only be reinvested at an effective annual rate of 2.1%. Find the accumulated value of Bob’s investment at the end of thirteen years. Round your answer to the nearest cent.

Subjects