Question

Your bank will pay you an interest rate of .112 percent per week. you want to have $23,500 in 8 years. How much will you have to deposit today? Assume 52 weeks per year.

Answer 1

The required answer is as below

If you want to have $ 23,500 in 8 years then you have to deposit $ 14,941.30 today. (see working notes)

Working Notes

(1) Calculation of rate of interest per annum

Weekly interest = 0.112 %

No of weeks per year = 52 weeks

Interest rate per year = Weekly interest rate X no of weeks per year

= 0.112 % X 52 weeks

= 5.824 %

(2) Calculation of present value

By formula PV = FV X [ PV Factor for n year, I per year ]

Where PV = Present Value

FV = Future Value

n = No of years

I = Interest rate per year

Given in the question

FV = $ 23,500

n = 8 years

i = 5.824 % per year

Now PV = 23,500 x [ PV Factor for 8 years, @ 5.824% per year]

= 23,500 X 0.6358

= $ 14,941.30