Question

(a) David Broke has $10,000 to deposit in his bank, Bancordia; if the bank is willing to pay annual interest of 2%, how much money will David Broke have in 5 years?

(b) Suppose the bank is willing to pay 1.5 % twice a year, how much money will David Broke have in 5 years?

(c) Imagine that after 5 years David Broke wants to buy a house; the bank is willing to loan him $120,000, which is unrelated to his saving. The bank expects David broke to make monthly payments by the end of each month for 30 years. How much should David Broke pay the bank on a monthly basis if the bank is charging him an interest of 3%?

(d) Amortize the loan to show how much principal and interest David will have to pay at the end of 3 years.

Please answer a, b, c and d in full sentences. thank you!

Answer 1

A) Amount Deposited at the beginning of the Year = $10,000

Rate of interest issued by Bank = 2%

Assumption 1 - Rate of interest is Simple

Total Earnings = Principle = $10000

Interest = $1000 ( $10000*2%*5 years)

Total = $11000

Assumption 2 = cumulative rate of interest

$A = P(1 + \frac{r}{n})^{nt}$

	=	final amount
	=	initial principal balance
	=	interest rate
	=	number of times interest applied per time period
	=	number of time periods elapsed

A = 10000(1+0.02/1)^1*5

A = $11,040

B) When the bank is willing to pay twice a year (assumed as cumulative interest)

The formula would be the same as above which is used for cumulative interest

A = 10000(1+ 0.03/2)^2*5

( Since 1.5% is interest for 6 months , the yearly interest would be 3%)

A = 11,605

C) Calculation of EMI

Formula = EMI = [P x R x (1+R)^N]/[(1+R)^N-1]

where P stands for the loan amount or principal, R is the interest rate per month [if the interest rate per annum is 11%, then the rate of interest will be 11/(12 x 100)], and N is the number of monthly instalments. When you use the above formula, you will get the same result that you will get in the Excel spreadsheet.

EMI = [120000 * 0.0025 * ( 1 + 0.0025)^360 ] / [(1 + 0.0025)^360 - 1]

EMI = 505.9248

D )

.Amortisation schedule for Three years

Year	Principle	Interest @ 0.25%	Total Due	EMI	outstanding Principle
1.00	1,20,000.00	300.00	1,20,300.00	505.92	1,19,794.08
2.00	1,19,794.08	299.49	1,20,093.56	505.92	1,19,587.64
3.00	1,19,587.64	298.97	1,19,886.60	505.92	1,19,380.68
4.00	1,19,380.68	298.45	1,19,679.13	505.92	1,19,173.21
5.00	1,19,173.21	297.93	1,19,471.14	505.92	1,18,965.21
6.00	1,18,965.21	297.41	1,19,262.63	505.92	1,18,756.70
7.00	1,18,756.70	296.89	1,19,053.59	505.92	1,18,547.67
8.00	1,18,547.67	296.37	1,18,844.04	505.92	1,18,338.11
9.00	1,18,338.11	295.85	1,18,633.96	505.92	1,18,128.03
10.00	1,18,128.03	295.32	1,18,423.35	505.92	1,17,917.43
11.00	1,17,917.43	294.79	1,18,212.22	505.92	1,17,706.30
12.00	1,17,706.30	294.27	1,18,000.56	505.92	1,17,494.64
13.00	1,17,494.64	293.74	1,17,788.38	505.92	1,17,282.45
14.00	1,17,282.45	293.21	1,17,575.66	505.92	1,17,069.73
15.00	1,17,069.73	292.67	1,17,362.41	505.92	1,16,856.48
16.00	1,16,856.48	292.14	1,17,148.62	505.92	1,16,642.70
17.00	1,16,642.70	291.61	1,16,934.31	505.92	1,16,428.38
18.00	1,16,428.38	291.07	1,16,719.45	505.92	1,16,213.53
19.00	1,16,213.53	290.53	1,16,504.06	505.92	1,15,998.14
20.00	1,15,998.14	290.00	1,16,288.13	505.92	1,15,782.21
21.00	1,15,782.21	289.46	1,16,071.66	505.92	1,15,565.74
22.00	1,15,565.74	288.91	1,15,854.65	505.92	1,15,348.73
23.00	1,15,348.73	288.37	1,15,637.10	505.92	1,15,131.17
24.00	1,15,131.17	287.83	1,15,419.00	505.92	1,14,913.08
25.00	1,14,913.08	287.28	1,15,200.36	505.92	1,14,694.43
26.00	1,14,694.43	286.74	1,14,981.17	505.92	1,14,475.25
27.00	1,14,475.25	286.19	1,14,761.43	505.92	1,14,255.51
28.00	1,14,255.51	285.64	1,14,541.15	505.92	1,14,035.22
29.00	1,14,035.22	285.09	1,14,320.31	505.92	1,13,814.39
30.00	1,13,814.39	284.54	1,14,098.92	505.92	1,13,593.00
31.00	1,13,593.00	283.98	1,13,876.98	505.92	1,13,371.05
32.00	1,13,371.05	283.43	1,13,654.48	505.92	1,13,148.56
33.00	1,13,148.56	282.87	1,13,431.43	505.92	1,12,925.50
34.00	1,12,925.50	282.31	1,13,207.82	505.92	1,12,701.89
35.00	1,12,701.89	281.75	1,12,983.65	505.92	1,12,477.72
36.00	1,12,477.72	281.19	1,12,758.92	505.92	1,12,252.99
Total Interest		10,466.29		18,213.29

Hence total interest paid for three years out of EMI = $10,466.29

Amount out of EMI which is used to offset the principle amount = $18213.29 - $10466.29 = $7,747