Question

the marcus hotel borrows $200000 from the spartan national bank the details are as follows:
a. Term of loan = 5 years
b. amortization rate = based on 10 years
c. frequency of payment = annual
d. interest rate = 6% required
1. prepare a loan amortization table for five years
2. what percentage of the loan was paid off over the five year period?
3. what was the total amount of interest paid?
4. what amount of interest will be paid over the 10 life of the loan?

a. how much be invested today to have 5,000 in five years if the interest rate is 6%?

b. at an effectives interest rate of 9%, what approximate amount will an investor have in 24 years if $5,000 is invested today?

c. Your sister, who is 6 years old today, just received a trust fund that will be worth $25,000 when she turns 21. IF the fund earns annual interest of 10% compounded quarterly, what is it today?

Answer 1

Answer 1:

Amount borrowed = $200000

a. Term of loan = 5 years
b. amortization rate = based on 10 years
c. frequency of payment = annual
d. interest rate = 6% required

To get yearly installments we will use PMT function of excel:

PMT (rate, nper, pv, fv, type)

PMT (6%, 10, -200000, 0, 0)

= $27173.59

Yearly Installment = $27173.59

Loan amortization table for five years:

Answer 2.

Percentage of the loan was paid off over the five year period = Repayment over 5 year / Loan amount *100

= $85,534.95 / $200,000 * 100

= 42.77%

Percentage of the loan was paid off over the five year period = 42.77%

Answer 3:

Total amount of interest paid over 5 year period = $50,333.01

Workings are as in table given in answer 1 above.

Answer 4 :

Amount of interest will be paid over the 10 life of the loan = Total amount of installments paid - Loan amount

= $27173.59 * 10 - $200,000

= $71735.92

= $71,736 (rounded off)

Answer 4-a:

Given:

FV = 5,000

Period = 5 years

Interest rate = 6%

PV = FV * 1 / (1 + Interest rate) ⁵

= $5000 * 1 / (1 + 6%) ⁵

= $3,736.29

Amount to be invested today = $3,736.29

Answer 4-b:

Interest rate = 9%

Period = 24 years

PV =$5,000

FV = PV * (1 + Interest rate) ^{Period in years}

= $5,000 * (1 + 9%) ²⁴

= $39,555.42

Amount will an investor have in 24 years if $5,000 is invested today = $39,555.42

Answer 4-c:

FV = $25,000

Period in years = 21 - 6 = 15

Period in quarters = 15 * 4 = 60

Quarterly interest rate = 10%/4 =2.5%

PV = FV * 1 / (1 + Interest rate) ^Period

= $25,000 * 1/ (1 + 2.5%) ⁶⁰

=$5,682.09

Amount today =$5,682.09