Question

Two sisters, Joan and Jocelyn decided to save money in funds that earns 14% compounded annually but on a different ways. Joan decides to save by making an end-of- year deposit of P1000 on the first year, P1100 on the second year and so on increasing the nest years deposit by 10th year. Jocelyn decided to save by just making equal deposits of P1400 annually for 10 years. Who has more savings at the end of 10 years?

Answer 1

Rate of interest = 14% compounded annually

Time = 10 years

John raises his end of year payment by $100 every year while Jocelyn pays $1,400 each year.

Saving structure of John:

First payment = $1,000. It will get interest for 10 years which makes its worth equals to $1,000 * (1.14)¹⁰ = $3,707.22

Second payment = $1,100. It will get interest for 10 years which makes its worth equals to $1,100 * (1.14)⁹ = $3,577.14

Third payment = $1,200. It will get interest for 10 years which makes its worth equals to $1,200 * (1.14)⁸ = $3,423.10

Forth payment = $1,300. It will get interest for 10 years which makes its worth equals to $1,300 * (1.14)⁷ = $3,252.94

Fifth payment = $1,400. It will get interest for 10 years which makes its worth equals to $1,400 * (1.14)⁶ = $3,072.96

Sixth payment = $1,500. It will get interest for 10 years which makes its worth equals to $1,500 * (1.14)⁵ = $2,888.12

Seventh payment = $1,600. It will get interest for 10 years which makes its worth equals to $1,600 * (1.14)⁴ = $2,702.33

Eighth payment = $1,700. It will get interest for 10 years which makes its worth equals to $1,700 * (1.14)³ = $2,518.62

Ninth payment = $1,800. It will get interest for 10 years which makes its worth equals to $1,800 * (1.14)² = $2,339.28

Tenth payment = $1,900. It will get interest for 10 years which makes its worth equals to $1,900 * (1.14)¹ = $2,166

Sum of John's savings after 10 years would be = $29,647.71

Saving structure of Jocelyn:

First payment = $1,400. It will get interest for 10 years which makes its worth equals to $1,400 * (1.14)¹⁰ = $5,190.12

Second payment = $1,400. It will get interest for 10 years which makes its worth equals to $1,400 * (1.14)⁹ = $4,552.72

Third payment = $1,400. It will get interest for 10 years which makes its worth equals to $1,400 * (1.14)⁸ = $3,993.62

Forth payment = $1,400. It will get interest for 10 years which makes its worth equals to $1,400 * (1.14)⁷ = $3,503.17

Fifth payment = $1,400. It will get interest for 10 years which makes its worth equals to $1,400 * (1.14)⁶ = $3,072.96

Sixth payment = $1,400. It will get interest for 10 years which makes its worth equals to $1,400 * (1.14)⁵ = $2,695.98

Seventh payment = $1,400. It will get interest for 10 years which makes its worth equals to $1,400 * (1.14)⁴ = $2,364.54

Eighth payment = $1,400. It will get interest for 10 years which makes its worth equals to $1,400 * (1.14)³ = $2,074.16

Ninth payment = $1,400. It will get interest for 10 years which makes its worth equals to $1,400 * (1.14)² = $1,819.44

Tenth payment = $1,400. It will get interest for 10 years which makes its worth equals to $1,400 * (1.14)¹ = $1,596

Sum of Jocelyn's savings after 10 years would be = $30,862.71

Thus Jocelyn would have more savings after 10 years.