Use the present value formula to determine the amount to be invested now, or the present value needed.

Question

The desired accumulated amount is $120,000 after 8 years investe

Answer 1

A=Pe^rt with r=annual rate of interest= 10%, t = 8 years, A=120000 e=about 2.718281828...

120000=Pe^(8(1/10) P= amount needed to investment at time t=0

120000/P = e^.8

ln(120000/P) =.8

ln2.23 = about .8

120,000/P = about 2.23

P = about 120000/2.23 = about $53,800

if interest is compounded continuously or approximately daily on a 53800 investment at 10% for 8 years

reaching $120,000

if compounded annually

A=P(1+r/n)^nt with n=1, r=.10, t=8, A=120000

120000=P(1.1^8)

P = 120000/1.1^8 = about $55,981 investment

for compounding between annually and continuously, such as quarterly or monthly

53800<P<55981 for 10% interest to reach 120000 in 8 years