Jose invests 6200 in a savings account that compounds intere

Jose invests $6200 in a savings account that compounds interest monthly at an APR of 5.1%. marta invests $6700 in a savings account that compounds interest annually at an APR of 4.8%. Who will have the higher accumulated balance after 5 years and after 20 yrs?

Solution

For nth year,

Accumulated balance for

Jose: A(5) = P(1+r/12)¹²ⁿ

Mart: A(n) = P(1+r)ⁿ

After 5 years:

Jose: A(5) = 6200(1+0.051/12)^12*5 = $7996.5

Marta: A(5) = 6700(1+0.048)⁵ = $8470

Hence, after 5 years Marta will higher accumulated balance

After 20 years:

Jose: A(20) = 6200(1+0.051/12)^12*20 = $17157

Marta: A(20) = 6700(1+0.048)²⁰ = $17112

Hence, after 20 years Jose will higher accumulated balance