SOLUTION: Aya and Sakura would like to buy a house and their dream home costs $500,000. Their goal is then to save $50,000 for a down payment and then would take out a mortgage loan for the

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Question 1190714: Aya and Sakura would like to buy a house and their dream home costs $500,000. Their goal is then to save $50,000 for a down payment and then would take out a mortgage loan for the rest. They plan to put their monthly saved amount in a conservative mutual fund that has a track record of a 5.2% rate of return. To be sure they don’t go spending this money on other things, they are going to move it into their investment account at the beginning of each month. Their hope is to be able to buy this home in 7 years.
What would their monthly savings amount have to be to reach this goal?
What will be the total interest earned be?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the payment required at the beginning of each month for 7 years will be $4433.32.

i used the financial calculator at https://arachnoid.com/finance/index.html

here are the results.



the inputs are:

present value 0
future value = 450,000
number of time periods = 7 * 12 = 84
interest rate % per time period = 5.2 / 12 = .433333....%
payments are at the beginning of each time period.

you then click on payment amount and you get -4,433.42.
this is rounded to the nearest penny.
it is negative because it's money that you are paying out at the beginning of each month.
the future value is positive because it is money that you will be receiving at the end of the investment period.

they shelled out a total of 84 * 4433.42 = 372,407.28

the present value of the payments is equal to 312,947.04.

the interest on the loan is 372,407.28 minus 312,947.04 = 59,460.24.

the online calculator rounds answers to the nearest penny.
with multiple things being done, this could generate some error.
i used my texas instruments business analyst calculator to do the same calculations.
this is what i got.
payment at the beginning of each month is equal to 4433.422978.
present value of the loan is equal to 312,947.0411.
84 payments of 4433.422978 is equal to 372,407.5302.
interest on the loan is 372,407.5302 minus 312,947.0411 = 59,460.4891.
4433.42978 rounds to 4433.42.
312,947.0411 rounds to 312,947.04
372,407.5302 rounds to 372,407.53.
59,460.4891 rounds to 59,460.49.

the results are slightly different.
if one set doesn't get you the right anser, then try the other set.
one of them should work.

let me know how you did.
theo
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Aya and Sakura would like to buy a house and their dream home costs $500,000. Their goal is then to save $50,000 for a down payment and then would take out a mortgage loan for the rest. They plan to put their monthly saved amount in a conservative mutual fund that has a track record of a 5.2% rate of return. To be sure they don’t go spending this money on other things, they are going to move it into their investment account at the beginning of each month. Their hope is to be able to buy this home in 7 years.
What would their monthly savings amount have to be to reach this goal?
What will be the total interest earned be? 
That person's WRONG!!

Correct amount: $492.60 at the beginning of each month, in order to accumulate $50,000 in 7 years, at 5.2% interest,

compounded monthly.

Answer 2: Multiply the $492.60 by 84 (payment periods), and then subtract $50,000 for this product to get interest earned over 

the 7-year period. 

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