Question

Answer in Excel

1. If I deposit $8,000 in a bank account that pays interest of 1.5%, compounded annually, how much will I have in the account after 10 years?

2. If I deposit $8,000 in a bank account that pays simple interest of 1.5%, how much will I have in the account after 10 years?

3. How would you explain the difference in the answers to the foregoing two problems, given that both banks pay interest at the same rate? Be specific.

4. You graduate from LIM and obtain a job paying an annual salary of $35,000. You estimate that you will receive a 10% salary increase each year. If you receive those salary increases, how much will you be earning after 4 years?

5. You deposit $5,000 in a bank account today that pays 2% interest, compound annually. You make no withdrawals from the account until 4 years have passed and then you withdraw all of the money that has accumulated in that account and deposit it into another bank that pays 3% interest compounded annually. You leave your money in the second bank for an additional 3 years. How much money will you have after the 7 years?

Answer 1

1)We are given the following information

PV	$              8,000.00
r	1.50%
n	10

We need to solve the following equation to arrive at the required FV

FV = PV X (1+r) FV = 8000 X (1+0.015)10 FV = 9284.33

So the FV is $9284.33

Excel formula is =FV(0.015,10,0,-8000)

PV value is input as a negative numebr because that is the amount you will have to deposit today to receive the FV in the future so it will be a cash outflow.

2) Amount after 10 years using simple interest is calculated below

PRT A = P + 100 A = Amount, P = Principle, R = Rate, T = time 8000 x 1.5 x 10 A = 8000+ 100 A = 9200

3)The difference in the FV of compound interest and the A of simple interest is because of the methos of interest used. Compound interest gives interest on the interest earned while the simple interest only gives interest on the principle amount. So the interest under compound interest goes on increasing each year while that remains constant under simple interest. For example, the interest of 1st year under both the methods will be 1.5% x 8000 = 120 but in the second year, the interest under compound interest will be calculated as 1.5% x (8000+120) = 121.80 while under simple interest, it will still be 120. This will continue for all 10 years and therefore the accumulation at the end of year 10 will be higher under compound interest as compared to simple interest.

We can create the schedule of interest under both methods to verify:

So in compound interest it will be as follows:

Year	Opening balance	Interest	Closing balance
1	$              8,000.00	$         120.00	$            8,120.00
2	$              8,120.00	$         121.80	$            8,241.80
3	$              8,241.80	$         123.63	$            8,365.43
4	$              8,365.43	$         125.48	$            8,490.91
5	$              8,490.91	$         127.36	$            8,618.27
6	$              8,618.27	$         129.27	$            8,747.55
7	$              8,747.55	$         131.21	$            8,878.76
8	$              8,878.76	$         133.18	$            9,011.94
9	$              9,011.94	$         135.18	$            9,147.12
10	$              9,147.12	$         137.21	$            9,284.33

• Opening balance of year 1 = 8000
• Opening balance of all other years = closing balance of previous years
• Interest = 1.5% x opening balance
• Closing balance = opening balance +interest

Under simple interest it will be as follows:

Year	Opening balance	Interest	Closing balance
1	$              8,000.00	$         120.00	$            8,120.00
2	$              8,000.00	$         120.00	$            8,240.00
3	$              8,000.00	$         120.00	$            8,360.00
4	$              8,000.00	$         120.00	$            8,480.00
5	$              8,000.00	$         120.00	$            8,600.00
6	$              8,000.00	$         120.00	$            8,720.00
7	$              8,000.00	$         120.00	$            8,840.00
8	$              8,000.00	$         120.00	$            8,960.00
9	$              8,000.00	$         120.00	$            9,080.00
10	$              8,000.00	$         120.00	$            9,200.00

• Opening balance of all years = 8000
• Interest = 1.5% x 8000
• Closing balance for year 1= opening balance +interest
• Closing balance for all other years = closing balance of previous year + interest of this year

4) You graduate from LIM and obtain a job paying an annual salary of $35,000. You estimate that you will receive a 10% salary increase each year. If you receive those salary increases, how much will you be earning after 4 years?

We are given the following information

PV	$            35,000.00
r	10.00%
n	4

We need to solve the following equation to arrive at the required FV

FV = PV > (1+r)" FV = 35000 X (1+0.14 FV = 51243.5

So by the end of 4rth year the salary will become 51243.5
Excel formula is =FV(0.10,4,0,-35000)

5) We are given the following information

PV	$              5,000.00
r	2.00%
n	4

We need to solve the following equation to arrive at the required FV

FV4 = PV (1+r)" FV4 = 5000 x (1 +0.02) FV4 = 5412.16

So the FV at the end of year 4 is $5412.16

Excel formula is =FV(0.02,4,0,-5000)

Then we take this amount and deposit it for 3 years at 3%

We are given the following information

PV	$              5,412.16
r	3.00%
n	3

We need to solve the following equation to arrive at the required FV

FV1 = FV4 x (1+r)" FV7 = 5412.16 x (1 + 0.03) FV1 = 5914.01

So the FV at the end of year 7 is $5914.01