Question

Linda Roy received a $205,000 inheritance after taxes from her parents. She invested it at 6.5% interest compounded quarterly for 8 years. A year later, she sold one of her rental properties for $215,000 and invested that money at 5.5% compounded semiannually for 7 years. Both of the investments have matured. She is hoping to have at least $505,000 in 12 years compounded annually at 4.5% interest so she can move to Hawaii.

Future Value of Inheritance Investment: $

Future Value of Rental Property Investment: $

Present Value of Final Investment: $

Future Value of Final Investment: $

Will she meet her goal?

Yes No

Answer 1

Formula: Future value = Principal*(1+r)^{^n}

Where r=rate of interest per period

n= number of periods

From the language of the question("Both of the investments have matured") it is clear that she made investment at period -8

and -7 And the investment have been maturity now means at period 0.

Value of Inheritance Investment now (at year 0):

Principal=205000

rate = 1.625% per period (i.e. 6.5/4)

n = 32 (i.e. 8*4)

Future value=205000*(1.1625)^{^32}

=205000*1.675011817

=343377.4

Future Value of Inheritance Investment at year end 12:

=343377.4*(1+.045)^{^12}

=343377.4*1.695881

=582327.4

Future Value of Rental Property Investment at year 0:

Principal=215000

rate = 2.75% per period (i.e. 5.5/2)

n = 14 (i.e. 7*2)

=215000(1+.0275)^{^14}

=215000*1.461994126

=314328.7

Future Value of Rental Property Investment at year end 12:

=314328.7*(1+.045)^{^12}

=314328.7*1.695881

=533064.3

Present Value of Final Investment:

Linda will invest what she has received from both of her investments now.(i.e. pv at period 0 of 20500 and 215000)

=343377.4+314328.7

=657706.2

Future Value of Final Investment(at period 12 from period 0):

=657706.2(1.045)^{^12}

=657706.2*1.695881433

=1115392

Will she meet her goal?

She require only 505000 in 12 years while she will get 1115392 at 12th year end so she will get her goal.