Question

True or False: Assume you wish to have a certain amount saved four years from now, and you plan to make a one-time deposit today in an interest-bearing account earning interest of 10%. As the compounding frequency of interest decreases, the amount you need to invest today in order to achieve your goal will decrease.

Answer 1

Answer:

True

Step-by-step explanation:

The formula for compound interest would be

$P(1+\frac{r}{100t} )^{nt}-P$

where t = no of quarters or half years or months or days per year and n = no of years.

Here n =4

We know  that compound interest gives interest for interest.  Hence if compounded half yearly, we get extra interest for second six months being the interest accrued in the first six months.  Hence semi annually will be more than annual.

On the same base, we find that quarterly is more than semi annual, and monthly compound interest will be more than quarterly.

In short we can say that as frequency increases we get more return hence to get a definite amount it is sufficient to invest a less amount.

Hence the given statement

As the compounding frequency of interest decreases, the amount you need to invest today in order to achieve your goal will decrease.

is true