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Homework answers / question archive / You are saving for a big purchase that you plan to make in 10 years
You are saving for a big purchase that you plan to make in 10 years. You will invest 100,000 today and then you will save 15,000 per year for the next ten years (first $15K investment will be made one year from now). If you expect to earn 6.5% on your investments, how much will you have in ten years
b. Same question as above, but you expect to earn 5% for the next five years and 8% for the final five years. How much will you have at the end of ten years?
Answer a.
Initial Investment = $100,000
Annual Deposit = $15,000
Time Period = 10 years
Interest Rate = 6.50%
Value at the end of 10 years = $100,000*1.0650^10 + $15,000*1.0650^9 + $15,000*1.0650^8 + … + $15,000*1.0650 + $15,000
Value at the end of 10 years = $100,000 * 1.0650^10 + $15,000 * (1.0650^10 - 1) / 0.0650
Value at the end of 10 years = $100,000 * 1.877137 + $15,000 * 13.494423
Value at the end of 10 years = $390,130.05
Answer b.
Initial Investment = $100,000
Annual Deposit = $15,000
Time Period = 10 years
Interest Rate for first 5 years = 5.00%
Interest Rate for last 5 years = 8.00%
Value at the end of 5 years = $100,000*1.05^5 + $15,000*1.05^4 + $15,000*1.05^3 + $15,000*1.05^2 + $15,000*1.05 + $15,000
Value at the end of 5 years = $100,000 * 1.05^5 + $15,000 * (1.05^5 - 1) / 0.05
Value at the end of 5 years = $100,000 * 1.276282 + $15,000 * 5.525631
Value at the end of 5 years = $210,512.67
Value at the end of 10 years = $210,512.67*1.08^5 + $15,000*1.08^4 + $15,000*1.08^3 + $15,000*1.08^2 + $15,000*1.08 + $15,000
Value at the end of 10 years = $210,512.67 * 1.08^5 + $15,000 * (1.08^5 - 1) / 0.08
Value at the end of 10 years = $210,512.67 * 1.469328 + $15,000 * 5.866601
Value at the end of 10 years = $397,311.18
