1) A zero-coupon bond is a security that pays no interest, and is therefore bought at a substantial discount from its face value

1) Computation of Price of Bond with continuous compounding:

Amount = Pe^(rt)

So, P = Amount / e^(rt)

Here,

P = Price of Bond = ?

Amount = Face Value = $1,200

r = Rate = 5%

t = Time = 9 Years

Substituting the values in formula;

P = $1,200/e^(5%*9) = $765.16 or $765

So, You should pay $765 today for a zero-coupon bond with a face value of $1,200 that matures in 9 years.

2) Computation of Interest Rate using Rate Function in Excel:

=rate(nper,pmt,-pv,fv)*12

Here,

Rate = Interest Rate = ?

Nper = 7 years*12 months = 84 months

PMT = 0

PV = $1

FV = $2

Substituting the values in formula:

=rate(84,0,-1,2)*12

Rate or Interest Rate = 9.94%

3) Computation of Number of Years using NPER Function in Excel:

=nper(rate,pmt,-pv,fv)

Here,

NPER = Number of Years = ?

Rate = (1+8%/2)^2 -1 = 8.16%

PMT = 0

PV = $50,000

FV = $1,000,000

Substituting the values in formula:

=nper(8.16%,0,-50000,1000000)

NPER or Number of Years = 38.19 years

So, It will take 38.19 years to reach your goal.

4) Computation of Future Value using FV Function in Excel:

=fv(rate,nper,pmt,-pv)

Here,

FV = Future Value = ?

Rate = 6%/4 = 1.5% compounded quarterly

Nper = 10 years * 4 quarters = 40 quarters

PMT = 0

PV = $300

Substituting the values in formula:

=fv(1.5%,40,0,-300)

FV or Future Value = $544.21