On january 1, 1980, moises deposited $1850 into a savings account paying 5.6% interest, compounded quarterly. if he hasn't made any additional deposits or withdrawals since then, and if the interest rate has stayed the same, in what year did his balance hit $3700, according to the rule of 72?

Question

Gerardo Barker

Business

14 August, 11:35

On january 1, 1980, moises deposited $1850 into a savings account paying 5.6% interest, compounded quarterly. if he hasn't made any additional deposits or withdrawals since then, and if the interest rate has stayed the same, in what year did his balance hit $3700, according to the rule of 72?

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Carlos Kirby · Answer 1

We first calculate for the effective interest of the given nominal interest that is compounded quarterly through the equation,

ieff = (1 + i/4) ^4 - 1

Substituting the known values,

ieff = (1 + 0.056/4) ^4 - 1 = 0.05718

To determine the future worth of a money invested with an interest that is compounded, the equation is,

F = P x (1 + ieff) ^n

where P is the present worth and n is the number of years.

For this item, we substitute the known terms in the derived second equation

3700 = (1850) x (1 + 0.05718) ^n

The value of n is 12.46 years.

Therefore, the money will be worth $3700 only on 1992.