Question

A sinking fund earning interest at j₂ = 6% now contains $10 000.

a) What quarterly equal deposits for the next 5 years will cause the sinking fund to grow to $20 000?

b) Within these 5 years from now, how much is in the sinking fund at the end of 4 years?

Answer 1

J2=6%

Interest is compounded halfyearly

Interest for half year=6/2=3%=0.03

Quarterly interest rate =r

(1+r)^2=(1+0.03)=1.03

1+r=(1.03^(1/2))= 1.014889

Quarterly Interest =r=0.014889=1.4889%

Future Value of current $10,000 after 5 years (5*4=20 quarters)

Quarterly interest rate=i =0.014889

Number of Quarters =N=20

Future Value(FV)=10000*((1+i)^N)=10000*(1.014889^20)= $13439.12

Balance Future Value Required =$20000-$13439.12=$6,560.88

Sinking Fund Factor =SFF=(A/F,i,N)=i/(((1+i)^N)-1)

i =0.014889

N=20

SFF=(A/F,1.4889%,20)= 0.014889/((1.014889^20)-1)= 0.043293

a)Quarterly equal deposit required =6560.88*0.043293=$284.04

Quarterly equal deposit required

$284.04

b) Amount in sinking fund at the end of 4 years:

i=Quarterly Interest =0.014889, N=Number of Quarters =4*4=16

Future value of $10,000at end of 4 years=10000*((1+i)^N)=10000*(1.014889^16)= $12,667.67

Compound amount factor (CAF)=(F/A,i,N)=(((1+i)^N)-1)/i

CAF=(F/A,1.4889%,16)=((1.014889^16)-1)/(0.014889)= 17.91705

Future value of $284.04 per quarter for 4 years=284.04*17.91705=$5,089.16

Amount in sinking fund at the end of 4 years= $12667.67+$5089.16= $17,756.83

Amount in sinking fund at the end of 4 years

$17,756.83