Question

URGENT PLEASE

A person wants to buy a house after seven years by making semiannual deposits of $40,000 in a bank account that pays 10%

1) compute the price of the house

2) three years later, directly after making the sixth payment, the person passed away. His son decided to buy the house on the same day that his father wanted to buy it.

However, he noticed that his fathers payments did not take into consideration the inflation rate of 5% that started three years ago and is expected to continue at the same rate for a long time. The son decided to make annual deposits at the start of each year, starting year four.

COMPUTE the amount of the annual payments that the son has to make in order to be able to buy the house taking into consideration the inflation rate.

Answer 1

1) The value of the house can be calculated by calculating the value of the deposits after 7 years.

For this, we use excel function FV =>  FV(5%,14,40000)

PMT= 40000

nper =14 ( Number of periods is 7 years*2 because of semiannual deposits)

rate = 0.05 ( 10%/2 for semi-annual period), we get

Future value of deposits = $783,945

We can also calculate using excel manually,

Year	Payment number	Deposit	FV factor (1.05^(14-Payment number))	Future value of the deposit
1	1	40000	1.885649142	75425.96569
1	2	40000	1.795856326	71834.25304
2	3	40000	1.710339358	68413.57432
2	4	40000	1.628894627	65155.78507
3	5	40000	1.551328216	62053.12864
3	6	40000	1.477455444	59098.21775
4	7	40000	1.407100423	56284.01691
4	8	40000	1.340095641	53603.82563
5	9	40000	1.276281563	51051.2625
5	10	40000	1.21550625	48620.25
6	11	40000	1.157625	46305
6	12	40000	1.1025	44100
7	13	40000	1.05	42000
7	14	40000	1	40000
			FV of deposits	783945.2796

Hence, the price of the house after 7 years is 783,945.27

2) Price of the house taking into consideration the inflation value = 783945*(1.05)^7 = 1,103,089

	Year	Payment number	Deposit	FV factor (1.05^(14-Payment number))	Future value of the deposit (After 7 years)
Payment by father	1	1	40000	1.885649142	75425.96569
1	2	40000	1.795856326	71834.25304
2	3	40000	1.710339358	68413.57432
2	4	40000	1.628894627	65155.78507
3	5	40000	1.551328216	62053.12864
3	6	40000	1.477455444	59098.21775
				The total value of deposits by father after 7 years	401980.9245

The total value of deposits by father after 7 years = 401,980

But the price of the house after 7 years = 1,103,089

Hence, the son needs to have a value = 1,103,089 - 401,980 = 701109 in order to buy the house ( with inflated price)

Using excel function, PMT, we input => PMT(0.1,4,0,701109,1)

rate = 10%

nper = 4 ( Since 4 years remaining and son making annual deposits)

PV = 0

FV = 701109 ( since we require this amount by end of the 7th year through son's deposits)

type = 1 ( Since deposits are made at the start of the year)

We get,

PMT = 137,335

Hence 137,335 is the amount of the annual payments that the son has to make in order to be able to buy the house taking into consideration the inflation rate.