Question

It is now January 1. You plan to make a total of 5 deposits of $400 each, one every 6 months, with the first payment being made today. The bank pays a nominal interest rate of 12% but uses semiannual compounding. You plan to leave the money in the bank for 10 years. Do not round intermediate calculations. Round your answers to the nearest cent.

1. How much will be in your account after 10 years?

   $  

2. You must make a payment of $1,432.04 in 10 years. To get the money for this payment, you will make five equal deposits, beginning today and for the following 4 quarters, in a bank that pays a nominal interest rate of 12% with quarterly compounding. How large must each of the five payments be?

   $  

Answer 1

Answer (a):

Deposit made at the begining of semiannual period = $400

Number of semiannual periods the deposits are made = 5

Semiannual interest rate = 12% / 2 = 6%

Let us first calculate the amount (FV) at the end 5th semiannual period (at the end of 2.5 years) = FV (rate, nper, pmt, pv, type)

= FV (6%, 5, -400, 0, 1)

= $2,390.127415

The money is kept in bank account for 10 years = 20 semiannual periods

To get amount at the end of 10 years, we need to calculate the FV of the amount $2,390.127415 after (20 - 5=) 15 semiannual periods

Amount in your account after 10 years = 2390.127415 * (1 + 6%) ¹⁵ = $5,728.08

Amount in your account after 10 years = $5,728.08

Answer (b):

Quarterly interest rate = 12% / 4 = 3%

Total period = 10 * 4 = 40 quarters

Future value required at the end of 10 years = $1,432.04

Deposits to be made at the start of each quarter for 5 quarters.

Value required at the end of quarter 5 = PV = FV / (1 + Periodic interest rate) ^{Number of periods}

= 1432.04 / (1 + 3%) ³⁵

= $508.92324

Amount of each of deposit = PMT (rate, nper, pv, fv, type)

= PMT (3%, 5, 0, -508.92324, 1)

= $93.07

Amount of each of deposit = $93.07