Question

Ann and Tom want to establish a fund for their​ grandson’s college education. What lump sum must they deposit at 12 ​% annual interest​ rate, compounded quarterly ​, in order to have ​20,000$in the fund at the end of 10 ​years? Answers 1. For Ann and Tom to have ​$20,000 at the end of 10 ​years, they must deposit a sum of $6,131.14. ### What is the principal? To calculate the sum of money they must deposit, use the compound interest formula. From the compound interest formula; P = A / ( 1 + r/n )^(nt) Given that; • Final amount A = 20,000 • Interest rate r = 12% = 12/100 = 0.12 • Compound n = quarterly = 4 • Time t = 10 years • Principal P = ? P = A / ( 1 + r/n )^(nt) P = 20,000 / ( 1 + 0.12/4 )^(4×10) P = 20,000 / ( 1.03)^40 P = 20,000 / 3.26203779 P =$6,131.14
Therefore, for Ann and Tom to have ​$20,000 at the end of 10 ​years, they must deposit a sum of$6,131.14.