Question

For the past 6 years Charlene Miller has made deposits of $300 at the end of every 6 months, earning interest at 5% compounded semi-annually. If she leaves the accumulated balance in an account earning 6% compounded quarterly, what will the balance be in Charlene’s account at the end of another 10 years?

Answer 1

The question has two parts. In first part,to find the accumulated value for semi-annual deposits for 6 years, use FV function in EXCEL

=FV(rate,nper,pmt,pv,type)

rate=5%/2=2.5% (2 semi-annual periods in a year)

nper=Total number of periods=6*2=12

pmt=300

pv=0

type=0 (payments are made at the end of 6 months)

=FV(2.5%,12,-300,0,0)

FV=$4138.67

==>In second part, this amount 4138.67 will earn an interest of 6% compounding quarterly for another 10 years. Use Future value formula, Future value=Present value*((1+(r/n))^(n*y))

Present value=4138.67

n=number of periods in a year=4

r/n=6%/4=1.5%

n*y=4*10=40 (y=number of years)

Future value=4138.67*((1+1.5%)^40)=4138.67*1.8140184=$7,507.62

The total balance be in Charlene’s account at the end of another 10 years=$7,507.62