Question

Investment X offers to pay you $5,000 per year with the first payment being received today. If you secure an 11% interest rate, how many years will it take you to reach $100,000 in savings? Please do not round, show the answer in decimal form.

Answer 1

Investment X offers to pay = $5,000 per year(first payment being received today)

interest rate = 11%

savings should be $100,000

here we we want to see whether how many years would it take to get $100,000 if we get $5000 per year and we invest it at 11% per annum

Formula: S = R((1+i)^n-1/i) (1+i)

Where

S = Future value of investment

R = Regular monthly investment

i = Interest rate assumed /12

n = Duration (number of months or number of years *12)

here we were calculating it for yearly

(substituting in the formula) note: we were receinving at the beginning of the year so we should substitte n with n+1

100,000=5000((1+0.11)^(n+1)-1/0.11)*(1+0.11)

1.11^(n+1)=2.98198198

adding logs on both sides

log 1.11=(1/n+1)log2.98

log 1.11=0.10436

log 2.98= 1.092588

n+1=10.4694

n=9.4694 years

it takes 9.4694 years you to reach $100,000 in savings