Question

Suppose you make deposits of $410 at the end of every three months for six years into an account earning 2.09%2.09% compounded quarterly. After these six years you leave the money in the account, without making additional deposits for another thirteen years invested at the same interest rate of 2.09%2.09% compounded quarterly.

How much will you have in the account after the first six years? (Round to the nearest cent.)

N =  I/Y = % P/Y =  C/Y =

PV = $ PMT = $ FV = $

How much will you have in the account after the entire nineteen years? (Round to the nearest cent.)

N =  I/Y = % P/Y=C/Y =

PV = $ PMT = $ FV = $

Answer 1

Amount after first six years = Future Value of Annuity of the deposit

Future Value = A(1+r)¹ + A(1+r)² + ......... + A(1+r)²⁴

Here A =Cash deposit

r = rate of interest on quarterly basis

As there will be 24 times of deposit in 5 years so the power is taken upto 24

Interest rate per quarter =  2.09% / 4 = 0.5225%

So the Future value after six years = 410(1+0.005225)¹ + 410(1+0.005225)² +........... + 410(1+0.005225)²⁴

= 10500 (rounded off to nearest cent)

After 19 years the amount will be calculated by compound interest formula,

A = P(1+r/n)^nt

where

• A = the future value of the investment/loan, including interest
• P = the principal investment amount (the initial deposit or loan amount)
• r = the annual interest rate (decimal)
• n = the number of times that interest is compounded per unit t
• t = the time the money is invested or borrowed for

A = 10454.55(1+0.0209/4)^4*13

= 13700 (rounded off to nearest cent)