down payment on a house, statistics homework help

Anonymous
timer Asked: May 31st, 2016
account_balance_wallet $10

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? – - - - - 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

strongboss5
School: Duke University

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:
𝑖′ = (1 + 𝑖)𝑛
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:
𝐼 = 𝑃𝑀𝑇 βˆ— 𝑖 βˆ— 𝑑
Where C = initial money (investment), i = interest rate, t = time

-

Ammortization:
π‘π‘Žπ‘¦π‘šπ‘’π‘›π‘‘ π‘Ÿπ‘Žπ‘‘π‘’ = 𝑃𝑀𝑇 βˆ—

𝑖
1 βˆ’ (1 + 𝑖)βˆ’π‘›

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? – - - - 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:


Frequency of investment of $388 = 15 days



Amount invested per month = 2*388 = $776



Interest rate = 6%, compounded monthly



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
𝑖′ = (1 + 𝑖)𝑛
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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Anonymous
awesome work thanks

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