Question

In an effort to save money for early retirement, an environmental engineering colleague plans to deposit $1,700 per month, starting one month from now, into a fixed rate account that pays 8% per year compounded quarterly. How much will be in the account at the end of 18 years?At the end of 18 years, the account will be $ ___.

Answer 1

Answer:

$268,696.93

Explanation:

Where an equal amount of money is saved periodically to earn interest at a particular rate of interest to accumulate a target amount in the future , it is called a sinking fund. The purpose could be for retirement, loan repayment or asset acquisition

The sum accumulated (deposit plus interest earned) at the end of the final period is known as the Future Value (FV) of the sinking fund.

The FV is determined as follows:

FV = A × ((1+r/m)^(n× m) - 1)/(r/m))

where FV- future value, A- annual cash flow, r-rate of return, n- number of years, m- number of compounding periods in a year.

so we can apply  this to our question

a = 1700, r - 8%= 0.08, m=4, n- 18

FV = 1,700 ×( (1+0.08/4)^(18 × 4) - 1)/(0.08/4))

     = 1700  × 158.0570

     =$268,696.93

The account will have $268,696.93 at he end of he 18 years