Question

Find the amount of each payment to be made into a sinking fund so that enough will be present to accumulate the following amount. Payments are made at the end of each period. The interest rate given is per period.

$77,000; money earns 4.5% compounded monthly for 1-2/3 years

Select one:
a. $719.42
b. $3714.64
c. $758.89
d. $1374.87

b. If you deposit $2000 into a fund paying 4% interest compounded monthly, how much can you withdraw at the end of each month for one year?

a. $177.48
b. $153.36
c. $189.12
d. $170.30
e. none of these

Answer 1

Results are below.

Step-by-step explanation:

a.

Future Value= $77,000

Number of periods= 1*12 + (2/3)*12= 20 months

Interest rate (i)= 0.045/12= 0.00375

To calculate the monthly deposit required, we need to use the following formula:

FV= {A*[(1+i)^n-1]}/i

A= monthly deposit

Isolating A:

A= (FV*i)/{[(1+i)^n]-1}

A= (77,000*0.00375) / [(1.00375^20) - 1]

Monthly deposit= $3,714.64

b.

Monthly deposit= $2,000

Interest rate= 0.04/12= 0.0033

Number of periods= 12 months

To calculate the monthly withdrawal, we need to use the following formula:

Monthly withdraw= (PV*i) / [1 - (1+i)^(-n)]

Monthly withdraw= (2,000*0.0033) / [1 - (1.0033^-12)]

Monthly withdraw= $170.26