Question

How much should you invest each month in order to have $300,000 if your rate of return is 8% compounded monthly and you want to achieve your goal in 40 years?

$

How much interest will you earn?

$

How much should you invest each month in order to have $300,000 if you want to achieve your goal in 20 years?

$

If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?

Answer 1

How much should you invest each month in order to have $300,000 if your rate of return is 8% compounded monthly and you want to achieve your goal in 40 years?

Payment required	=	FV*r /[(1+r)^n -1]
Future value	FV	300,000.00
Rate per period	r
Annual interest		8%
Number of interest payments per year		12
Interest rate per period		0.08/12=
Interest rate per period		0.667%
Number of periods	n
Number of years		40
Periods per year		12
number of periods		480
Period payment	=	300000*0.006667/ [(1+0.006667)^480 -1]
	=	85.94

Each month payment is $85.94

How much interest will you earn?
Interest = Future value - total payments

Future value	=		300,000.00
Less: total payments:
Per period payment		85.94
× number of payments		480.00
Total payments		41,251.20	41,251.20
Interest earned			258,748.80

How much should you invest each month in order to have $300,000 if you want to achieve your goal in 20 years?

Payment required	=	FV*r /[(1+r)^n -1]
Future value	FV	300,000.00
Rate per period	r
Annual interest		8%
Number of interest payments per year		12
Interest rate per period		0.08/12=
Interest rate per period		0.667%
Number of periods	n
Number of years		20
Periods per year		12
number of periods		240
Period payment	=	300000*0.006667/ [(1+0.006667)^240 -1]
	=	509.32

Payment required is $509.32

If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?

FV of annuity	=	P * [ (1+r)^n -1 ]/ r
Periodic payment	P=	$                  509.32
rate of interest per period	r=
Rate of interest per year		8.0000%
Payment frequency		Once in 1 months
Number of payments in a year		12.00
rate of interest per period		0.08*1/12	0.6667%
Number of periods
Number of years		10
Number of payments in a year		12
Total number of periods	n=	120
FV of annuity	=	509.32* [ (1+0.00667)^120 -1]/0.00667
FV of annuity	=	93,178.07

Future value of annuity after ten years is $93,178.07

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