Question

In solving the following problem :

The local bank pays 4% interest on savings deposits. In a nearby town, the bank pays 1% per quarter. A man who has $3000 to deposit wonders whether the higher interest paid in the nearby town justifies driving there.

1. How much will the man receive after 2 years if he used the local bank? The answer is closest to:

		$3123
		$3246
		$3060
		$3186

Q2)

What sum of money now is equivalent to $8250 two years hence, if interest is 4% per 6-month period? The answer is closest to:

Hint : 4% per 6 month means semi annual periods so the n does not equal 2 anymore !

		$8,923
		$7,052
		$8,580
		$9,651

Answer 1

1.

To calculate the amount of money the man receive after 2 years if he used the local bank, we need to use the Single payment compound amount factor (i.e., we need to find the future value of $3,000 at 4% interest rate).

The formula for Single payment compound amount factor is

FV = PV * (F/P, i, N)

Where, PV = $3,000

(F/P, i, N) = (1 + i)^N

i = 4% or 0.04

N = 2 year

So, FV = $3,000 * (1 + 0.04)²

FV = $3,000 * (1.082) = $3246.

So, the man will receive after 2 years if he used the local bank is:

$3246.

2.

In this case, we need to find the present value of $8,250. For this purpose, we need to use the Single payment present worth factor.

The formula for Single payment present worth factor is

PV = FV * (P/F, i, N)

Where, FV = $8,250

(P/F, i, N) = 1 / [(1 + i)^N]

i = 4% or 0.04

N = 2 years = (2 * 2) semin annual periods = 4

So, PV = $8,250 * [1 / {(1 + 0.04)⁴}]

PV = $8,250 * 0.8548 = $7,052.

So, the sum of money now is equivalent to $8250 two years hence, if interest is 4% per 6-month period is:

$7,052.