Question

You plan to make five deposits of $1,000 each, one every 6 months, with the first payment being made in 6 months. You will then make no more deposits. If the bank pays 6% nominal interest, compounded semiannually, how much will be in your account after 3 years? One year from today you must make a payment of $4,000. To prepare for this payment, you plan to make two equal quarterly deposits (at the end of Quarters 1 and 2) in a bank that pays 6% nominal interest compounded quarterly. How large must each of the two payments be?

Answer 1

Answer:

Check the calculation below.

Explanation:

a) Amount in account after 3 years:

= $1,000 (1+ 0.03)5 + $1,000 (1+ 0.03)4+ $1,000 (1+ 0.03)3 + $1,000 (1+ 0.03)2 + $1,000 (1+ 0.03)

= $1,159.27 + 1,125.51 + 1,092.73 + 1,060.90 + 1,030

= $5,468.40

b) Calculation of amount of payment:

Let the amount of each of two payment be "P".

Now, $4,000 = P (1 + 0.015)3 + P (1 + 0.015)2

or,$4,000 = 1.0457 P + 1.0302 P

or, P = $4,000 / 2.0759

or, P = 1,927 (Approx)