Williams FIN 3301 Unit 5 AGN

1

Williams FIN 3301 Unit 4

Student’s Name

Institution Affiliation

Course

Insturcotr’s Name

Date

Williams FIN 3301 Unit 4

Question 1

Annual payment required = Loan amount / PVIFA (6%,5) Loan Amount = $350,000 PVIFA (6%,5) = 4.212

Amount required = $350,000/4.212 = 83,095.92

The payment appears to be excessive, as the entire amount paid, including interest, is $415,479.6, which is a large sum given the 6% interest rate.

Question 2

a)

The formula to calculate periodic loan amount is

(P * r * (1+r)n)/((1+r)n-1)

Where P is the principal Amount

R is the periodic interest rate

n is the number of periods

Now, P = 459,000

r = 0.025/12 = 0.0020833

Time is 30*12 = 360 Months

Thus, the monthly loan payments is

=459,000* 0.002083 * (1.002083)360/((1.002083)360 -1)

= 459,000* 0.002083 * 1.8968

= 1,813.5

b) Therefore, incase amortization time is 15 years then n= 15*12 = 180 months

Monthly loan Payment = 495,000* 0.006667 * (1.002083)180/ ((1.002083)180 -1)

= 495,000 * 0. * 3.306921/2.306921

= 495,000 * 0.002083 * 1.4543368

= 495,000*0.002083*3.201009

=3,300.51

c) Because the loan must be returned faster, the monthly payment amount automatically increases as the loan period shortens. However, the amount of interest paid decreases as the loan period shortens.

Higher loan periods lower monthly payments more cumulative interest

Minimal loan time, more monthly payments and less cumulative interest

Question 3

a. Information provided:

Future value= $750,000

Time= 20 years

Interest rate= 12%

Enter the below in a financial calculator to compute the present value:

FV= 750,000

N= 20

I/Y= 12

Using a PV calculator to calculate the present value

The value obtained is $77,750.07

Thus, the present value of her goal is $77,750.07

b. Data are given:

Future value= $750,000

Time= 15 years

Interest rate= 12%

Place the following in a financial calculator to calculate the present value:

FV= 750,000

N= 15

I/Y= 12

Using a PV calculator to calculate the present value

The value obtained is $137,022.20.

Thus, the present value of her aim is $137,022.20.

The present value here is more when the period to accumulate $750,000 is lower.

Question 4

a. Future Value

Interest rate = 6%

Number of periods = 4

Payment per period = $475

Future Value = (1+0.06)*475*[(1+r) 4-1)]/0.06

=1.06*475[4.374616)

=$2,202.62

b. Difference

Interest rate = 6%

Number of periods = 4

Payment per period = $475

An ordinary Annuity

Future = 475* [(1+0.06) 4-1)]/0.06

= $2,077.94

Thus, difference is obtained by

=2,202.62-2,077.94

=$124.68

Question 5

a)

Present worth or value of bond=Present value of coupon payments+ Present value of face value

Present worth or value of bond=Coupon payment*((1-(1/(1+r)^n))/r)+Face value/(1+r)^n

Here

Face value =1000

n=number of periods to maturity=5*2=10 semiannual periods

r- Interest rate per period=YTM per period=12/2=6% semi annual

Semi Annual Coupon payment=coupon rate *face value/2=9.5%*1000/2=47.5

Placing values in formula

Present worth or value of bond=47.5*((1-(1/(1+6%)^10))/6%)+1000/(1+6%)^10

=349.60+558.39

Therefore, Present worth/value of bond=$907.99

b- in case interest is paid yearly

Present worth or value of bond=Present value of coupon payments+ Present value of face value

Present worth or value of bond=Coupon payment*((1-(1/(1+r)^n))/r)+Face value/(1+r)^n

Here

Face value =1000

n=number of periods to maturity=5 (annual periods)

r- interest rate per period=YTM per period=12% annual

Annual Coupon payment=coupon rate *face value=9.5%*1000/2=95

placing values in formula

Present worth or value of bond=95*((1-(1/(1+12%)^5))/12%)+1000/(1+12%)^5

=342.45+567.43

Calculating to obtain

Present worth of bond=909.88

As can be seen, the present value of a bond decreases when interest is paid semiannually rather than annually since the effective interest rate rises in semiannual periods, lowering the bond's present value.