How much principal must be invested today for 5 years, during a period when the

Question

How much principal must be invested today for 5 years, during a period when the inflation rate is 2%, if the investor is in the 25% Federal and 4% State tax bracket for ordinary income but taxed at a 15% Federal rate for dividend income, to accumulate $10,000 in the following cases: The principal is invested in a certificate of deposit that pays annual interest of 6%? The principal is invested in a stock that retains its share price and pays an annual dividend of 6%? The principal is invested in a municipal bond (on which no state tax is levied) that pays annual interest of 5%?

Explanation / Answer

GIVEN,

TIME (T)=5 YEARS

INFLATION RATE (I)=0.02

TAX FOR ORDINARY INCOME= 0.25+0.04=0.29

TAX FOR DIVIDEND INCOME =0.15

AMOUNT TO BE ACCUMULATE (A) = $10,000

(I) ANNUAL INTEREST RATE (R)= 0.06

INTERST RATE CONSIDERING INFLATION=( 1.06 * 1.02)-1=0.0812

RATE NET OF TAX=0.0812(1-0.29)=0.057652

APPLYING FORMULA,

A=P(1+RT)

$10,000=P(1+0.057652*5)

$10,000=P*1.28826

SO,PRINCIAL TO BE INVESTED P =$10,000/1.28826 =$ 7,762( ROUNDED OFF)

(II)DIVIDEND RATE (R)=6%

R TAKING INTO ACCOUNT INFLATION RATE= (0.06*0.02)-1=0.0812

RATE NET OF TAX=0.0812(1-0.15)=0.06902

APPLYING FORMULA,

A=P(1+RT)

$10,000=P(1+0.06902*5)

$10,000=P*1.3451

PRINCIPAL (P)=$10,000/1.3451

=$7,434(ROUNDED OFF)

(III)INTEREST RATE (R)=0.05

INTEREST RATE CONSIDERING INFLATION=(1.05*1.02)-1=0.071

RATE AFTER FEDERAL TAX OF 25%= 0.071(1-0.25)=0.05325

APPLYING FORMULA,

A=P(1+RT)

$10,000=P(1+0.05325*5)

$10,000=P*1.26625

SO PRINCIPAL TO BE INVESTED = $10,000/1.26625=$7,897(ROUNDED OFF)

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