SOLUTION: PLEASE HELP ME I NEED HELP UNDERSTANDING HOW TO SOLVE THEM STEP BY STEP.... Problem #8 Which of the following investments is larger after 19 years? (a) $7500 is deposited

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Question 86995: PLEASE HELP ME I NEED HELP UNDERSTANDING HOW TO SOLVE THEM STEP BY STEP....
Problem #8
Which of the following investments is larger after 19 years?
(a) $7500 is deposited annually and earns 4.5% interest compounded annually.
(b) $600 is deposited monthly and earns 4.5% interest compounded monthly.
Problem #9
Find monthly payment.
In order to purchase a home, a family borrows $26000 at 10.8 % for 15 yr. What is their monthly payment? Round the answer to the nearest cent.
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Problem #8
Which of the following investments is larger after 19 years?
(a) $7500 is deposited annually and earns 4.5% interest compounded annually.
(b) $600 is deposited monthly and earns 4.5% interest compounded monthly.
-------
Compare their growth using compound interest formula and the the Future Value formula:
Compound Interest: FV = (principal)(1+r/n)^(nt)
FV = 7500(1+0.045/1)^(1*19)
-------
Future Value: FV = (periodic payment)[(1+i)^n -1]/i
where periodic payment = $600; n=12*19 ; i=0.045/12
======================
Problem #9
Find monthly payment.
In order to purchase a home, a family borrows $26000 at 10.8 % for 15 yr. What is their monthly payment? Round the answer to the nearest cent.
--------
Use this annuity formla:
balance = (loan amt)(1+i)^n - [P/i][(1+i)^n - 1]
You want the balance to be zero;
loan amt=26000
i=0.108/12
n=12*15
Solve for P=monthly payment.
--------
I get $292.26
============
Cheers,
Stan H.

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
#8
a)
Let p=7500, r=0.045, n=1, and t=19 and plug them into

Start with the given expression
Divide 0.045 by 1 to get 0.045
Multiply the exponents 1 and 19 to get 19
Add 1 and 0.045 to get 1.045
Raise 1.045 to the 19 th power to get 2.30786031084919
Multiply 7500 and 2.30786031084919 to get 17308.9523313689

So the return is $17,308.95

b)

Let p=600, r=0.045, n=12, and t=19 and plug them into

Start with the given expression
Divide 0.045 by 12 to get 0.00375
Multiply the exponents 12 and 19 to get 228
Add 1 and 0.00375 to get 1.00375
Raise 1.00375 to the 228 th power to get 2.3476172358424
Multiply 600 and 2.3476172358424 to get 1408.57034150544

So the return is $1408.57


So the $7,500 investment is larger after 19 years

----------------------------------------------------------------------
#9
To calculate the monthly payment, use this formula:

where P is the principal (i.e. the amount loaned out), R is the periodic interest rate (in decimal form) and n is the number of monthly payments

First lets calculate R:

To find the periodic interest rate, divide the APR (this is given as 10.8%) by the number of months in a year. Also divide the APR by 100 to convert the percentage to a decimal





Start with the given expression

Add to get 1.009

Multiply to get -180

Raise 1.009 to the -180 power

Subtract to get 0.800662008823199

Multiply to get 234

Divide 234 by 0.800662008823199 to get 292.258153154949


So the monthly payment, rounded to the nearest cent, is roughly $292.26
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