Question

In: Finance

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 :

a

$95,940.99

b

$10,559.01

please rate.

jeff jeffy answered 2 years ago
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