You want to take a dream vacation in 3.5 years. You plan to save up $5,000 in your vacation sinking fund. Assume an interest rate of 8% compounded annually. How much will you have to save if you make a lump sum deposit to the sinking fund (i) during the year or (ii) at the beginning of the year?

The formula for calculating the Monthly payments P for the sinking fund is as follows:

where,

P = Monthly payments to be made

A = Total amount to be accumulated

i = Interest rate for given time period

n = Number of time period

Assuming interest is applied at the beginning of each period.

We are given two scenarios.

In this scenario, as some of the year is already passed (assume 6 months), to complete the time period of 3.5 years the interest will compound 3 times (as the 0.5 year payments can be adjusted in the remaining part of the first year and no interest is applied on it). Hence, the interest will be applied 3 times.

For this case, the interest will be applied 4 times to complete the time period of 3.5 years for payment.

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