down payment on a house, statistics homework help
Question Description
These are the questions I need answered. Thank you.
1. In order to accumulate enough money for a down payment on a house, a couple deposits $388 per month into an account paying 6% compounded monthly. If Payments are made at the end of each period, how much money will be in the account in 5 years? β     Round to the nearest dollar.
2. Acme Annuities recently offered an annuity that pays 5.1% compounded monthly. What equal monthly deposit should be made into this annuity in order to have $60,000 in 17 years?     Round to the nearest cent
3. A company estimates that it will need $142,000 in 17 years to replace a computer. If it establishes a sinking fund by making fixed monthly payments into an account paying 4.5% compounded monthly, how much should each payment be?     Round to the nearest cent
4. Find i (the rate per period) and n (the number of periods) for the following loan at the given annual rate.
Monthly payments of $277.00 are made for 10 years to repay a loan at 6.25% compounded monthly.      type and integer or decimal rounded to four decimal places as needed
5. Find i (the rate per period) and n (the number of periods) for the following loan at the given annual rate.
Annual payments of $3,400 are made for 10 years to repay a loan at 8.95% compounded annually.     type integer as a decimal
6. Find i (the rate per period) and n (the number of periods) for the following loan at the given annual rate.
Quartarly payments of $725 are made for 13 years to repay a loan at 11.6% compounded quarterly.     type integer as a decimal
7. Find i (the rate per period) and n (the number of periods) for the following loan at the given annual rate.
Semiannual payments of $4,500 are made for 17 years to repay a loan at 7.35% compounded semiannually.     type an integer or a decimal rounded to four decimal places as needed
8. Solve the following problem.
N=31; i=0.025; PMT=$243; PV=?
PV=$ (round to two decimal places)
9. Solve the following problem.
PV=$147,154; n=113; i=0.012; PMT=?;
PMT=$ (round to two decimal places)
10. Use the formula for the present value of an ordinary annuity or the amortization formula to solve the following problem.
PV=$9,000; i=0.005; PMT=$650; n=?
N= (round up to the nearest integer)
Tutor Answer
Dear student,Please find enclosed a doc file with the answers to the 10 questions.
Running head: STATISTICS HOMEWORK
1
STATISTICS HOMEWORK
(NAME)
(COURSE)
(DATE)
STATISTICS HOMEWORK
2
Table of contents
No se encontraron entradas de tabla de contenido.
STATISTICS HOMEWORK
3
Theoretical background
The formulas that you need to solve the different exercises are:

Coumpound interest rate:
πβ² = (1 + π)π
Where i' = compound interest rate, i = interest rate, n = time periods (e.g. months or year
depending if the interest rate is compounded monthly or annually). Since i should be
expressed in the same time period, if n is compounded monthly we would need to divide
i/12 as interest rates are typically expressed annually.

Simple interest:
πΌ = πππ β π β π‘
Where C = initial money (investment), i = interest rate, t = time

Ammortization:
πππ¦ππππ‘ πππ‘π = πππ β
π
1 β (1 + π)βπ
STATISTICS HOMEWORK
4
Exercises
1. In order to accumulate enough money for a down payment on a house, a couple deposits
$388 per month into an account paying 6% compounded monthly. If Payments are made
at the end of each period, how much money will be in the account in 5 years? β    Round to the nearest dollar.
To solve this problem, we will use the formula of compound interest presented in the
theoretical background. Hence, according to the available data we know:
ο§
Frequency of investment of $388 = 15 days
ο§
Amount invested per month = 2*388 = $776
ο§
Interest rate = 6%, compounded monthly
ο§
Period = 5 years = 5*12 = 60 months
The compounded interest rate means that the interest rate in a specific month n is
calculated by the formula
πβ² = (1 + π)π
Considering an annual rate of 6% and that the compound is done monthly, we know i =
0.06/12. Thus, the compound interest rate at a given month n is i' = 1.005n.
On the other hand, we are doing 2 monthly investments of $338, such that the total
amount of money invested in a given month n is calculated as 2Β·338Β·n = 676n.
Taking this into account, the total money in t...
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