Jasica Parker would like to have 56000 to buy a new car in 5

Jasica Parker would like to have $56,000 to buy a new car in 5 years. To accumulate $56,000 in 5 years, how much should she invest monthly in a sinking fund with 9% interest compounded monthly?

The montly invested payment is?

Solution

We know that if an account has an annual interest rate of r% and which is compounded m times per year, then we have i = r/m is the interest rate per compounding period.

Now to accumulate amount A in an account after say t years or n = m*t periods, by making payments of P at the end of each period then,

P = A*[ {i / (1 + i)^n – 1 } ]

In our question, compounding of interest and payment to the account is done monthly, so we have

A = 56000
i = r / m = 9% /12 = 9/100*12 = 3/400 = 0.0075
n = m*t = 5*12 = 60

P = ?

So,
P = 56000*[ {0.0075 / (1 + 0.0075)^60 – 1 } ]
= 420 / {(1.0075)^60 – 1}
= 420 / ( 1.5657 – 1 )
= 420 / 0.5657
= 742.44
So, she has to invest $742.44 monthly in the sinking fund.