ngner mteger yl What is the minimum number of yearend deposi

ngner mteger yl. What is the minimum number of year-end deposits that have to be made before the total value of the deposits is at least ten times greater than the value of a single year-end deposit if the interest rate is 12 %?

Solution

If the periodic payment is (P), the future value or maturity value of periodic deposits in (FV), and rate on interest is (n), then number of period it will take for deposits to accumulate to FV is

n = log (1 + iF/P)/ log(1 + i)

Where,

                  Periodic payment (P) = $1000

                  Future value or maturity value (FV) = $10000

                  Interest rate (i) = 12.5% (Annually)

Let\'s put the values in the formula to solve for n

n = log(1 + 0.125* 10000/ 1000)/ log(1 + 0.125)

    = log(1 + 1250/ 1000)/ log(1.125)

    = log(1 + 1.25)/ log(1.125)

    = log(2.25)/ log(1.125)

    = 0.352182518111362/ 0.0511525224473813

    = 6.88 years