Question

When Michael is born, four uncles decide to save money for his future in different ways: Uncle A: He deposits $50 on Michael's first birthday, and every subsequent birthday. Uncle B: He deposits $15 on Michael's first birthday, and every subsequent birthday he deposits $5 more than the previous year. Uncle C: He deposits $40 on Michael's first birthday, and every subsequent birthday he deposits 5% more than the previous year. Uncle D: At Michael's birth he deposits $300 in a savings account which offers 2.7% interest compounded quarterly. By the time Michael is 21 years old, which uncle has saved the most money for him?

Answer 1

By the time Michael is 21 years old, Uncle C has saved the most money.

Step-by-step explanation:

Uncle A = $50 on Michael's first birthday, and same on each birthday

When Michael is 21 years of old, His Uncle A will save = $50 x 21 = $1,050

Uncle B = $15, and $5 more than the previous year. It means 15, 20, 25...

When Michael is 21 years of old, His Uncle B will save = $1,365

Here is the sequence = (15+20+25+30+35+...............+100+105+110+115)

Uncle C = $40, and 5% more than the previous year. It means $40 x 1.05 = $42 in the 2nd year.

When Michael is 21 years of old, His Uncle C will save = $1,428.77 (See the image below to get the proper explanation)

Uncle D = $300. It offers 2.7% interest compounded quarterly. When Michael is 21 years of old, His Uncle D will save = $527.88

Using the Future value, we can determine Uncle D's savings. Hence,

FV = PV ×
`(1 + (i)/(m) )^(n*m)`

FV = $300 ×
`(1 + (0.027)/(4) )^(21*4)`

FV = $300 × 1.7596

FV = $527.88