Question

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

You must make a payment of $1,788.04 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 10% with quarterly compounding. How large must each of the five payments be? $

Answer 1

1]

Account value after 5 deposits (2 years) is calculated using FV function in Excel :

rate = 5% (converting annual rate into semiannual rate. semiannual rate = annual rate / 2 = 10% / 2 = 5%)

nper = 5 (number of deposits)

pmt = 300 (deposit amount)

FV is calculated to be $1,657.69

This amount is compounded semiannually at 10% interest per annum for 8 years (16 semiannual periods). The account value at the end of 10 years = $1,657.69 * (1 + 5%)¹⁶ = $3,618.53

2]

With quarterly compounding, the quarterly interest rate = annual rate / 4 = 10% / 4 = 2.5%

number of quarters in 8 years = 8 * 4 = 32

The amount required to be in account at the end of 2 years from now = $1,788.04 / (1 + 2.5%)³² = $811.36

The quarterly deposit is calculated using PMT function in Excel :

rate = 2.5% (quarterly rate)

nper = 5 (number of payments)

pv = 0 (beginning amount is zero)

fv = 811.36 (required amount at end of 2 years)

PMT is calculated to be $154.36

Each payment must be $154.36