Question

You want to buy a house within 3 years, and you are currently saving for the down payment. You plan to save $10,000 at the end of the first year, and you anticipate that your annual savings will increase by 5% annually thereafter. Your expected annual return is 9%. How much will you have for a down payment at the end of Year 3? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

It will have 34,351 available for a down payment at the end of Year 3

Step-by-step explanation:

savings:

first year: 10,000

second year 10,000 + 5% = 10,000 x 1.05 = 10,500

third years (10,000 + 5%) + 5% = 10,500 x 1.05 = 11,025

return on Invetment

The first saving will capitalize for two years at 9%

`Principal \: (1+ r)^(time) = Amount`

First year: 10,000.00

time 2.00

rate 0.09

`10000 \: (1+ 0.09)^(2) = Amount`

Amount 11,881.00

The second savings will capitalize for one yeat at 9%

Second year: 10,500.00

time 1.00

rate 0.09

`10500 \: (1+ 0.09)^(1) = Amount`

Amount 11,445.00

Total amount:

11,881 + 11,445 + 11,025 = 34,351