Question

With wages from a summer job you make a total of 11 deposits at $1,338 per month into a savings account earning 8% compounded monthly. At the time of the last deposit, you close the savings account and invest all the money in stocks with the intention of leaving the stocks alone for the subsequent 19 years (dividends automatically are reinvested). The stocks are expected to provide an average annual return of 19.11% compounded monthly. When you finally sell the stocks, how much do you get?

What is the annual capital gains yield expected over the next year for a 12 year bond with 9.7% coupon rate paying the coupons every six months and selling at $1,145 (enter answer as a percentage)?

Answer 1

1]

Future value of annuity = P * [(1 + r)n - 1] / r,

where P = periodic payment. This is $1,338

r = periodic rate of interest. This is (8%/12). We divide by 12 since we need to convert the annual rate into monthly rate)

n = number of periods. This is 11

Value of savings account after 11 deposits  = $1,338 * [(1 + (8%/12))11 - 1] / (8%/12)

Value of savings account after 11 deposits  = $15,218.54

Future value of lump sum = present value * (1 + (r/n))n*t

where r = annual rate of interest. This is 19.11%

n = number of compounding periods per year. This is 12, as the compounding is monthly.

t = number of years. This is 19.

Value of stocks after 19 years = $15,218.54 * (1 + (19.11%/12))12*19

Value of stocks after 19 years = $558,250.04

When you finally sell the stocks, you get $558,250.04