A regular saving of 500 is made into a sinking fund at the...

A regular saving of $\$ 500$ is made into a sinking fund at the start of each year for 10 years. Determine the value of the fund at the end of the tenth year on the assumption that the rate of interest is
(a) $11 \%$ compounded annually
(b) $10 \%$ compounded continuously

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Key Concepts

Continuous Compounding

Continuous compounding is the theoretical limit of compound interest, where interest is added an infinite number of times per period. This results in an exponential growth model described by the formula A = Pe^(rt), where the exponential function reflects the effect of continuously compounding interest over time.

Sinking Fund

A sinking fund is a financial strategy where regular deposits are made to accumulate a specific amount of money in the future, often used to repay debt or replace a large asset. It involves scheduled payments that earn interest over time, ensuring that sufficient funds are available when needed.

Annuity Due

An annuity due is a series of equal payments made at the beginning of each period. This timing results in each payment having an extra period to earn interest compared to payments made at the end of the period. The future value of an annuity due is calculated by adjusting the standard annuity formula to account for this additional compounding period.

Compound Interest

Compound interest refers to the process where interest is not only earned on the initial principal but also on the accumulated interest from previous periods. This effect causes the investment or savings to grow at an exponential rate over time as interest earnings become part of the principal for subsequent periods.

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