Question

A bank offers a retirement annuity that earns 4% APR, compounded monthly. Each person wants to have at least $200,000 in the account when they retire. For each retirement plan described, determine: the monthly deposit, the total length of time they spent investing, the amount in their account at the end of the investing time, the total amount of money they invested, and the total amount of interest they earned. Round monthly deposits up to the cents place and other dollar amounts down to the cents place; for the amount of time spent investing, express your answer in years and months, rounded up to the whole month.
a. Lavon wants to deposit $200 per month.
b. Micha wants to deposit $100 per month.

Answer 1

a

Number of payments required to achieve future value	=	log [(FV × r/ PMT) +1] /log(1+r)
Future value	FV	200,000.00
Rate per period	r
Annual interest		4.0%
Number of payments per year		12
Interest rate per period		0.04/12=
Interest rate per period		0.333%
Payment per period	PMT	$                                   200.00
Number of payments	=	log [( 200000×0.00333/200) +1]/ long(1+ 0.00333)
	=	440.63
Future value	=		200,000.00
Less: total payments:
Per period payment		200.00
× number of payments		440.63
Total payments		88,126.78	88,126.78
Interest earned			111,873.22
Monthly deposit		200.00
Total lengh of time in years		36.72
Amount in account at end		200,000.00
Money invested		88,126.78
Interest earned		111,873.22

36.72 years is 36 years 9 months (rounded off).

b

Number of payments required to achieve future value	=	log [(FV × r/ PMT) +1] /log(1+r)
Future value	FV	200,000.00
Rate per period	r
Annual interest		4.0%
Number of payments per year		12
Interest rate per period		0.04/12=
Interest rate per period		0.333%
Payment per period	PMT	$                                   100.00
Number of payments	=	log [( 200000×0.00333/100) +1]/ long(1+ 0.00333)
	=	612.08
Future value	=		200,000.00
Less: total payments:
Per period payment		100.00
× number of payments		612.08
Total payments		61,208.25	61,208.25
Interest earned			138,791.75
Monthly deposit		100.00
Total lengh of time in years		51.01
Amount in account at end		200,000.00
Money invested		61,208.25
Interest earned		138,791.75

51.01 years is 51 years and one month.

Please rate.