a) It is now January 1. You plan to make a total of 5 deposits of $300 each, one

Question

a) It is now January 1. You plan to make a total of 5 deposits of $300 each, one every 6 months, with the first payment being made today. The bank pays a nominal interest rate of 14% but uses semiannual compounding. You plan to leave the money in the bank for 5 years. How much will be in your account after 5 years? Round your answer to the nearest cent.

$

b) You must make a payment of $1,828.74 in 10 years. To get the money for this payment, you will make 5 equal deposits, beginning today and for the following 4 quarters, in a bank that pays a nominal interest rate of 8% with quarterly compounding. How large must each of the 5 payments be? Round your answer to the nearest cent.

$

Explanation / Answer

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You must make a payment of $1,061.34 in 10 years. To get the money for this payment, you will make 5 equal deposits, beginning today and for the following 4 quarters, in a bank that pays a nominal interest rate of 14% with quarterly compounding. How large must each of the 5 payments be? Round your answer to the nearest cent.
$

1. Value after 5 payments are made = 300*(1+14%/2)^4+300*((1+14%/2)^4-1)/(14%/2) = 1725.22

This is after a period of 2 years

So the value after 5 years (i.e. a further period of 3 more years) = 1725.22*(1+14%/2)^(3*2) = $ 2589.09

2. PV of the 1061.34 today = 1061.34/(1+14%/4)^(10*4) = 268.065

Let each payment be $ X

PV of the 5 payments of $ X = X*(1-1/(1+14%/4)^4)/(14%/4) + X = 4.673*X

So 4.673*X = 268.065, which means X = $ 57.36

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