The information technology (IT) department has recently completed a major refurbishment and upgrade of the city’s data center, at a cost of $10,145,825. The chief information officer (CIO) has informed the central budget office that the IT department will need to do the same kind of upgrade in 5 years, and he expects the total cost of that project to be 10% more than this year’s project, accounting for better future technology and future increases in costs. The city does not expect to have enough funding available to pay for the refurbishment in 5 years and must put money away during each of the next 4 years to meet this need. How much money should the city put aside in each of the next 4 years to be able to pay for the data center refurbishment 5 years from now, assuming the city can invest the money at a 4.5% interest rate? calculate FV, Rate, Years, Denominator, PMT and now, use the Excel function Excel f(x) to get the same result (I need this part)
Amount required for next project after 5 years | = | $10,145,825*110% | |||
= | 11160407.5 | ||||
Amount at the end of 4 years (FV) (saving is done only in 4 years) | = | 11160407.5/1.045 | |||
= | 10679815.79 | ||||
Rate | = | 4.50% | |||
time | = | 4years | |||
FV | = | P*FVAF(rate,time) | |||
10679815.79 | = | P*FAVF(4.5%,4) | |||
10679815.79 | = | P*4.2782 | |||
10679815.79/4.2782 | = | p | |||
P | = | 2,496,334 | |||
Amount to be saved Each year (4 years) | = | $2,496,333.92 | |||
Verification | |||||
Year | Opening bal | Amount saved | Interest earned @ 4.5% | Total balance | |
1 | 0 | $2,496,333.92 | $0.00 | $2,496,333.92 | |
2 | $2,496,333.92 | $2,496,333.92 | $112,335.03 | $5,105,002.87 | |
3 | $5,105,002.87 | $2,496,333.92 | $229,725.13 | $7,831,061.92 | |
4 | $7,831,061.92 | $2,496,333.92 | $352,397.79 | $10,679,793.62 | |
5 | $10,679,793.62 | No saving year 5 | $480,590.71 | $11,160,407.33 |
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