Question

1. Deposits of $1200.00 are being made at the beginning of every 3 months for 10 years. At the end of the 10 year term the accumulated amount is left in the fund for a further 5 years (the deposits have stopped). What is the maturity value at the end of the 15 year term if the interest rate for the full period is 5.25% compounded semiannually?

2. Find the monthly payments for a mortgage of $200,000 that is to be repaid in 20 years if the interest rate being charged is 4.75% compounded semiannually. How much interest will have been paid over the 20 years and how much interest would have been paid if the amortization period were 15 years

Deposits of $1200.00 are being made at the beginning of every 3 months for 10 years. At the end of the 10 year term the accumulated amount is left in the fund for a further 5 years (the deposits have stopped). What is the maturity value at the end of the 15 year term if the interest rate for the full period is 5.25% compounded semiannually? Find the monthly payments for a mortgage of $200,000 that is to be repaid in 20 years if the interest rate being charged is 4.75% compounded semiannually. How much interest will have been paid over the 20 years and how much interest would have been paid if the amortization period were 15 years

Answer 1

1)

$1200 given every 3 months

Interest rate - 5.75% Interest Rate for SemiAnnual Compoundind = 2.63%

Total Time Period of Deposit: 15 Years

Based on Table Below: Total Maturity Amount After 15 years will be$82,028.32

PayOut No.	Amount	Deposited At (years)	Total Time	Compunding Time Period	Total Value
1	1200	0	15	30	$       2,610.82
2	1200	0.25	14.75	29.5	$       2,577.21
3	1200	0.5	14.5	29	$       2,544.04
4	1200	0.75	14.25	28.5	$       2,511.29
5	1200	1	14	28	$       2,478.96
6	1200	1.25	13.75	27.5	$       2,447.05
7	1200	1.5	13.5	27	$       2,415.55
8	1200	1.75	13.25	26.5	$       2,384.46
9	1200	2	13	26	$       2,353.77
10	1200	2.25	12.75	25.5	$       2,323.47
11	1200	2.5	12.5	25	$       2,293.56
12	1200	2.75	12.25	24.5	$       2,264.04
13	1200	3	12	24	$       2,234.90
14	1200	3.25	11.75	23.5	$       2,206.13
15	1200	3.5	11.5	23	$       2,177.73
16	1200	3.75	11.25	22.5	$       2,149.70
17	1200	4	11	22	$       2,122.03
18	1200	4.25	10.75	21.5	$       2,094.71
19	1200	4.5	10.5	21	$       2,067.75
20	1200	4.75	10.25	20.5	$       2,041.13
21	1200	5	10	20	$       2,014.86
22	1200	5.25	9.75	19.5	$       1,988.92
23	1200	5.5	9.5	19	$       1,963.32
24	1200	5.75	9.25	18.5	$       1,938.05
25	1200	6	9	18	$       1,913.10
26	1200	6.25	8.75	17.5	$       1,888.48
27	1200	6.5	8.5	17	$       1,864.17
28	1200	6.75	8.25	16.5	$       1,840.17
29	1200	7	8	16	$       1,816.49
30	1200	7.25	7.75	15.5	$       1,793.10
31	1200	7.5	7.5	15	$       1,770.02
32	1200	7.75	7.25	14.5	$       1,747.24
33	1200	8	7	14	$       1,724.75
34	1200	8.25	6.75	13.5	$       1,702.55
35	1200	8.5	6.5	13	$       1,680.63
36	1200	8.75	6.25	12.5	$       1,659.00
37	1200	9	6	12	$       1,637.64
38	1200	9.25	5.75	11.5	$       1,616.56
39	1200	9.5	5.5	11	$       1,595.75
40	1200	9.75	5.25	10.5	$       1,575.21

2)

Suppose Monthly Payout is $x

Then for 20 years EMI $x will be paid 240 times

Months	1	2	3	4	...	240
Paid Amount	x	x	x	x		x
Time Period for Interest Rate	=1/6=0.1667	0.33	0.5	0.667		40
Multplier	1/(1+2.375%)^0.1667	1/(1+2.375%)^0.33	1/(1+2.375%)^0.5	1/(1+2.375%)^0.667		1/(1+2.375%)^40

Multipliers above Follow a geometirc progression(GP) hence sum of all of them will

a*(1-r^240)/(1-r) where a & r = 1/(1+2.375%)^0.1667 = 0.9961

Sum of GP = 155.353

Now applying this to equation above

200000 = x * 155.353

=> x = 200000/155.353 = $1287.39

Now if period of payment is 15years then

Sum of GP will be : 128.959

=> Monthly Payout for 15 years will be 200000/128.959 = $1550.89