Question

Annuity and Compound Interest problem!
how to solve for interest rate (NOT using tvm solver on a calculator) girl puts $300 each month into an ordinary annuity for 20 years. interest was compounded monthly. at the end of 20 years, the annuity was worth $147126. what was the annual interest rate?

Im using the compound interest formula P(1+i)=A
Im getting .0261496485 --> 2.6% but that is wrong, the answer is suppose to be 6.5%.. Did i make an error?
Here is my work:
300(1+I)^240 = 147,126
(1+i)^240 = 147,126/300
(1+i)^240 = 490.42
240√(1+i)^240 = 240√(490.42)
1+i = 240√(490.42)
i= 240√(490.42) -1
i = .0261496485
how do i solve the problem?

Answer 1

do you know convolution?

Answer 2

or solving first order DE?

Answer 3

Is this not a matter of simply finding an annual effective rate?

Answer 4

actually this is an annuity problem

Answer 5

i am not familiar with convolution in mathematic terms.. and yes @kirbykirby it is an annuity problem

Answer 6

help?? @Luis_Rivera @AccessDenied , @Hero .....anyone?

Answer 7

Use the formula

FV = C*[ ( (1+i)^n - 1)/i ]

where in this case

FV = 147126

C = 300

i = x (this is unknown and we're solving for it)

n = 12*20 = 240


so this means


FV = C*[ ( (1+i)^n - 1)/i ]


turns into


147126 = 300*[ ( (1+x)^240 - 1)/x ]


which can be rewritten as


147126x = 300( (1+x)^240 - 1)


From here, I would use a graphing calculator to solve for x (since you have an exponent of 240, it's going to be tough to solve by hand)

Answer 8

well i dont have to solve the entire problem b y hand.. i have to show work -- i can use a calc. lol THANK YOUU

Answer 9

you're welcome