Question

a)         Jasmine makes quarterly deposits of $1,000 into a savings account that pays 4 percent compounded monthly. How much money will she have in her account in 25 years?

2. Jasmine makes monthly deposits of $1,000 into an investment account that pays 4 percent compounded quarterly. How much money will she have in her account in 25 years?

3. Gabriel deposits $1,000 at the beginning of each month into an investment account that pays 4 percent compounded monthly. How much money will he have in his account in 25 years?

Answer 1

A.

Quarterly deposits = $1000

Effective quarterly rate R = (1+4%/12)^3 - 1 = 1.0033%

Number of quarters in 25 years = 100

So,

Future value of deposits after 25 years = 1000*(1.010033^100 - 1)/.010033

Future value of deposits after 25 years = $170802.92 or $170803

So, value of deposits in 25 years is $170802.92 or $170803.

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B.

A.

Monthly deposits = $1000

Effective monthly rate R = (1+4%/4)^(1/3)  - 1 = .3322%

Number of months in 25 years = 300

So,

Future value of deposits after 25 years = 1000*(1.003322^300 - 1)/.003322

Future value of deposits after 25 years = $513119.96 or $513120

So, value of deposits in 25 years is $513119.96 or $513120.

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A.

It is a case of annuity due as payment takes place in the beginning of the month.

Monthly deposits = $1000

Monthly rate = 4%/12

Number of months in 25 years = 300

So,

Future value of deposits after 25 years = (1000*((1+4%/12)^300 - 1)/(4%/12))*(1+4%/12)

Future value of deposits after 25 years = $515843.3 or $515843

Hence , value of deposits in 25 years would be $515843.3 or $515843.