Lucy set up a savings fund for her son's education so that she would be able...

Lucy set up a savings fund for her son's education so that she would be able to withdraw $1,775 at the beginning of every month for the next 5 years. The fund earns 4.35% compounded quarterly.

a. What amount should she deposit today to allow for the $1,775 periodic withdrawals?

$77,923.75

$95,595.71

$95,940.99

$78,771.17

b. How much interest would she earn in this investment?

$95,940.99

$10,559.01

$106,500.00

$10,904.29

Solutions

Expert Solution

Particulars	Amount
Given APR	4.35%
Given compounding frequency per year	4
Effective annual rate	4.421%
(1+ 0.0435/4)^4 -1
Required compounding frequency per year	12
Req period effective rate	0.3612%
(1+ 0.04421475)^1/12 -1
Required APR	4.33433%
0.00361194*12

	Present value of annuity due=	P* [ [1- (1+r)^-(n-1) ]/r ] + P


P=	Periodic payment	1,775.00


r=	Rate of interest per period:
	Annual rate of interest	4.33433%
	Frequency of payment	once in every 1 months
	Payments per year	12/ 1=	12
	Interest rate per period	0.0433433/12=	0.361%

n=	number of payments:
	Number of years	5
	Payments per year	12

	number of payments	60


	Present value of annuity=	1775* [ [1- (1+0.003612)^-(60-1)]/0.003612 ] +1775

	Present value of annuity=	95,940.98


	Total withdrawals	106,500.00
	Interst portion	10,559.02

Answers :

$95,940.99

$10,559.01

please rate.

jeff jeffy answered 1 year ago

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