Question

Answer the following questions.

1. A company decided to take a 1,000,000 Dhs as a loan from a bank. The negotiations between the company and the bank ended by an agreement stating that the company will take this interest as a compound interest with an interest rate of 6% and that the company will pay equal installments for the next 8 years to return back the loan and its interest to the bank.

a. Determine the annual equal amount of payment by the company to the bank.

b. Determine the total amount of interest the company is going to pay after the 8 years.

c. After the fifth payment (after 5 years) the company had a financial problem and as a result went into a new negotiation with the bank administration which agreed to convert the rest of the amount that was supposed to be paid for the next three years to a pure compound interest loan that can be paid at the end of the three years with the same interest rate of 6% per year.

- What is the new principle for the new loan (P2)?

- What is the amount of money that is going to be paid due to the new loan after the new three years (F2)?

- What is the total amount of interest that is going to be paid after the company fully succeeds to return back the whole loan with its interest? In other words, what is the total amount of interest paid during the 8 years of the loan?

Answer 1

Answer:-

given:-

Rate of interest (r) = 6%

Years (n) = 8

Annual frequency = 1

Loan amount (PV)= 1000000

(a) :- to calculate PMT, formula is as follow

PV= PMT x 1-(1+r)^-n/r

Using PV ,n and r we get

1000000 = PMT x 1-(1+0.06)^-8/0.06

PMT = 60000/1-(1.06)^-8

PMT = 161,035.94

So the annual payment= 161,035.94

(b) :- Interest amount calculated as follows

Interest= PMT x n - PV

Using above value we get

Interest = 161035.94 x 8 - 1000000

Interest = 288,287.52

Total interest paid is = $288,287.52

(c) :- we first need to calculate the amortization schedule of the original plan.

Year	opening balance	PMT	Interest	principal Repayment	Closing Balance
1	$1000000	$161,035.94	$60,000	$101,035.94	$898,964.06
2	$898,964.06	$161,035.94	$53,937.84	$107,098.10	$791,865.96
3	$791,865.96	$161,035.94	$47,511.96	$113,523.99	$678,341.97
4	$678,341.97	$161,035.94	$40,700.52	$120,335.42	$558,006.55
5	$558,006.55	$161,035.94	$33,480.39	$127,555.55	$430,451.00
6	$430,451.00	$161,035.94	$25,827.06	$135,208.88	$295,242.12
7	$295,242.12	$161,035.94	$17,714.53	$143,321.42	$151,920.70
8	$151,920.70	$161,035.94	$9,115.24	$151,920.70	$0.00
	Total	$12,88,287.54	$288,287.52	$1,000,000

Closing balance= opening balance+ loan - principal repayment

PMT is calculated as per the above formula

Interest = 0.06 x opening balance

Principal repayment = PMT - interest

So at the end of 5 year the closing balance

= $430,451.00

This becomes the principal amount of the new loan.

Now we need to find the future value of this new principal amount to find out the amount payable at the end of 3 year.

Given information:-

New principal= (PV)= $430,451.00

Rate of interest (r) = 6%

Years = 3

To calculate Future value(FV) we need to solve following equation.

FV = PV x (1+r)^n

Putting value we get

FV = 430451 x ( 1+0.06)^3

= 430451 x (1.06)^3

= 430451 x 1.191016

FV = 512,674.03

Interest rate on the new loan = FV - PV

= 512,674 - 430451

= $82,223.03

* Total interest = interest on old loan + interest on new loan

* Interest on old loan is the sum of interest coloum for first 5 years of in the above amortization schedule.

* $60,000+ $53,937.84 +$47,511.96 + $40,700.52 +$33,480.39 = $235,630.71

* This is different from the total interest calculated in part ( b) which is the interest of the total 8 year loan.

* Total interest = $235,630.71 + $82,223.03

= $317,853.74